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DFG Schwerpunktprogramm 1276

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Liste von Veröffentlichungen aus den SPP-Einzelprojekten. Keine Gewähr für Vollständigkeit.

Die Liste enthält derzeit 190 Veröffentlichungen.

## 2015 |

Riechelmann,; Wacker,; Beheng,; Etling,; Raasch, Influence of turbulence on the drop growth in warm clouds, Part II: sensitivity studies with a spectral bin microphysics and a Lagrangian cloud model (Artikel) Meteorologische Zeitschrift, 2015. @article{Riechelmann2015, name = {Influence of turbulence on the drop growth in warm clouds, Part II: sensitivity studies with a spectral bin microphysics and a Lagrangian cloud model}, author = {Riechelmann, T. and Wacker, U. and Beheng, K.D. and Etling, D. and Raasch, S.}, url = {http://www.schweizerbart.de/papers/metz/detail/prepub/84723/Influence_of_turbulence_on_the_drop_growth_in_warm?af=crossref}, year = {2015}, date = {2015-02-02}, journal = {Meteorologische Zeitschrift}, abstract = {Raindrops in warm clouds grow faster than predicted by classical cloud models. One of the possible reasons for this discrepancy is the influence of cloud turbulence on the coagulation process. In Part I (Siewert et al., 2014) of this paper series, a turbulent collision kernel has been derived from wind tunnel experiments and direct numerical simulations (DNS). Here we use this new collision kernel to investigate the influence of turbulence on coagulation and rain formation using two models of different complexity: a one-dimensional model called RAINSHAFT (height as coordinate) with cloud microphysics treated by a spectral bin model (BIN) and a large-eddy simulation (LES) model with cloud microphysics treated by Lagrangian particles (a so called Lagrangian Cloud Model, LCM). Simulations are performed for the case of no turbulence and for two situations with moderate and with extremely strong turbulence. The idealized 0- and 1-dimensional runs show, that large drops grow faster in the case turbulence is taken into account in the cloud microphysics, as was also found by earlier investigations of other groups. For moderate turbulence intensity, the acceleration is only weak, while it is more significant for strong turbulence. From the model intercomparison it turns out, that the BIN model produced large drops much faster than the LCM, independent of turbulence intensity. The differences are larger than those due to a variation in turbulence intensities. The diverging rate of formation of large drops is due to the use of different growth models for the coagulation process, i.e. the quasi-stochastic model in the spectral BIN model and the continuous growth model in LCM. From the results of this model intercomparison it is concluded, that the coagulation process has to be improved in future versions of the LCM. The LES-LCM model was also applied to the simulation of a single 3-D cumulus cloud. It turned out, that the effect of turbulence on drop formation was even smaller as the turbulence within the cloud was weaker than prescribed in the idealized cases. In summary, the use of the new turbulent collision kernel derived in Part I does enhance rain formation under typical turbulence conditions found in natural clouds but the effect is not very striking.}, } Raindrops in warm clouds grow faster than predicted by classical cloud models. One of the possible reasons for this discrepancy is the influence of cloud turbulence on the coagulation process. In Part I (Siewert et al., 2014) of this paper series, a turbulent collision kernel has been derived from wind tunnel experiments and direct numerical simulations (DNS). Here we use this new collision kernel to investigate the influence of turbulence on coagulation and rain formation using two models of different complexity: a one-dimensional model called RAINSHAFT (height as coordinate) with cloud microphysics treated by a spectral bin model (BIN) and a large-eddy simulation (LES) model with cloud microphysics treated by Lagrangian particles (a so called Lagrangian Cloud Model, LCM). Simulations are performed for the case of no turbulence and for two situations with moderate and with extremely strong turbulence. The idealized 0- and 1-dimensional runs show, that large drops grow faster in the case turbulence is taken into account in the cloud microphysics, as was also found by earlier investigations of other groups. For moderate turbulence intensity, the acceleration is only weak, while it is more significant for strong turbulence. From the model intercomparison it turns out, that the BIN model produced large drops much faster than the LCM, independent of turbulence intensity. The differences are larger than those due to a variation in turbulence intensities. The diverging rate of formation of large drops is due to the use of different growth models for the coagulation process, i.e. the quasi-stochastic model in the spectral BIN model and the continuous growth model in LCM. From the results of this model intercomparison it is concluded, that the coagulation process has to be improved in future versions of the LCM. The LES-LCM model was also applied to the simulation of a single 3-D cumulus cloud. It turned out, that the effect of turbulence on drop formation was even smaller as the turbulence within the cloud was weaker than prescribed in the idealized cases. In summary, the use of the new turbulent collision kernel derived in Part I does enhance rain formation under typical turbulence conditions found in natural clouds but the effect is not very striking. |

Schlegel,; Stiller,; Bienert,; Maas,; Queck,; Bernhofer, Large-Eddy Simulation Study of the Effects on Flow of a Heterogeneous Forest at Sub-tree Resolution (Artikel) Boundary-Layer Meteorology, 154, Seite(n): 27-56, 2015. @article{Schlegel2015, name = {Large-Eddy Simulation Study of the Effects on Flow of a Heterogeneous Forest at Sub-tree Resolution}, author = {Schlegel, F. and Stiller, J. and Bienert, A. and Maas, H.-G and Queck, R. and Bernhofer, C.}, url = {10.1007/s10546-014-9962-y}, year = {2015}, date = {2015-01-01}, journal = {Boundary-Layer Meteorology}, volume = {154}, pages = {27-56}, abstract = {Abstract The effect of three-dimensional plant heterogeneity on flow past a clearing is investigated by means of large-eddy simulation. A detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 328m length and 172m width at the field site “Tharandter Wald”, near the city of Dresden, Germany. The scanning data are used to produce a highly resolved, three-dimensional plant area distribution representing the actual canopy. Hence, the vegetation maintains a rich horizontal and vertical structure including the three-dimensional clearing. The scanned plant area density is embedded in a larger domain, which is filled with a heterogeneous forest generated by the virtual canopy generator of Bohrer et al. (Tellus B 59:566–576, 2007). Based on forest inventory maps and airborne laser scanning, the characteristics of the actual canopy are preserved. Furthermore, the topography is extracted from a digital terrain model with some modifications to accommodate for periodic boundary conditions. A large-eddy simulation is performed for neutral atmospheric conditions and compared to simulations of a two-dimensional plant area density and an one-year-long field experiment conducted at the corresponding field site. The results reveal a considerable influence of the plant heterogeneity on the mean velocity field as well as on the turbulent quantities. The three-dimensional environment, e.g., the oblique edges combined with horizontal and vertical variations in plant area density and the topography create a sustained vertical and cross-flow velocity. Downstream of the windward forest edge an enhanced gust zone develops, whose intensity and relative position are influenced by the local canopy density and, therefore, is not constant along the edge. These results lead us to the conclusion that the usage of a three-dimensional plant area distribution is essential for capturing the flow features inside the canopy and within the mixing layer above.}, } Abstract The effect of three-dimensional plant heterogeneity on flow past a clearing is investigated by means of large-eddy simulation. A detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 328m length and 172m width at the field site “Tharandter Wald”, near the city of Dresden, Germany. The scanning data are used to produce a highly resolved, three-dimensional plant area distribution representing the actual canopy. Hence, the vegetation maintains a rich horizontal and vertical structure including the three-dimensional clearing. The scanned plant area density is embedded in a larger domain, which is filled with a heterogeneous forest generated by the virtual canopy generator of Bohrer et al. (Tellus B 59:566–576, 2007). Based on forest inventory maps and airborne laser scanning, the characteristics of the actual canopy are preserved. Furthermore, the topography is extracted from a digital terrain model with some modifications to accommodate for periodic boundary conditions. A large-eddy simulation is performed for neutral atmospheric conditions and compared to simulations of a two-dimensional plant area density and an one-year-long field experiment conducted at the corresponding field site. The results reveal a considerable influence of the plant heterogeneity on the mean velocity field as well as on the turbulent quantities. The three-dimensional environment, e.g., the oblique edges combined with horizontal and vertical variations in plant area density and the topography create a sustained vertical and cross-flow velocity. Downstream of the windward forest edge an enhanced gust zone develops, whose intensity and relative position are influenced by the local canopy density and, therefore, is not constant along the edge. These results lead us to the conclusion that the usage of a three-dimensional plant area distribution is essential for capturing the flow features inside the canopy and within the mixing layer above. |

## 2014 |

Jasor,; Wacker,; Beheng,; Polifke, Modeling artifacts in the simulation of the sedimentation of raindrops with a Quadrature Method of Moments (Artikel) Meteorologische Zeitschrift, 23, 4, Seite(n): 369-385, 2014. @article{Jasor2015, name = { Modeling artifacts in the simulation of the sedimentation of raindrops with a Quadrature Method of Moments}, author = {Jasor, G. and Wacker, U. and Beheng, K.D. and Polifke, W}, url = {https://www.schweizerbart.de/papers/metz/detail/23/84225/Modeling_artifacts_in_the_simulation_of_the_sedimentation_of_raindrops_with_a_Quadrature_Method_of_Moments?l=DE }, year = {2014}, date = {2014-04-01}, journal = {Meteorologische Zeitschrift}, volume = {23}, number = {4}, pages = {369-385}, abstract = {The Quadrature Method of Moments (QMoM) is applied to a one-dimensional test case for sedimentation of raindrops. Comparison of the results with a reference spectral method exhibits discrepancies (“step patterns”) that must be considered as modeling artifacts. As the QMoM has been demonstrated to be effective and accurate in various contexts, the origin of these artifacts is investigated and found to be related to the transport of the quadrature abscissas. Further test cases are considered to examine the influence of different initial conditions on the development of the modeling artifacts. The study shows that these artifacts are inherent to the application of QMoM in pure sedimentation context. }, } The Quadrature Method of Moments (QMoM) is applied to a one-dimensional test case for sedimentation of raindrops. Comparison of the results with a reference spectral method exhibits discrepancies (“step patterns”) that must be considered as modeling artifacts. As the QMoM has been demonstrated to be effective and accurate in various contexts, the origin of these artifacts is investigated and found to be related to the transport of the quadrature abscissas. Further test cases are considered to examine the influence of different initial conditions on the development of the modeling artifacts. The study shows that these artifacts are inherent to the application of QMoM in pure sedimentation context. |

von Harlander U., Larcher Th. Wright Hoff Alexandrov; Egbers, Orthogonal decomposition methods to analyze PIV, LDA and thermography data of a thermally driven rotating annulus laboratory experiment (Buch) ., ., ., 2014. (BibTeX) @book{Harlander2014, name = { Orthogonal decomposition methods to analyze PIV, LDA and thermography data of a thermally driven rotating annulus laboratory experiment}, author = {Harlander, U., von Larcher, Th., Wright, G.B., Hoff, M., Alexandrov, K. and Egbers, C.}, editor = {von Larcher, Th. and Williams, P.}, note = {accepted for publishing, to appear in 2014 }, year = {2014}, date = {2014-04-23}, journal = {AGU Book Modelling Atmospheric and Oceanic flows: insights from laboratory experiments and numerical simulations}, volume = {.}, number = {.}, publisher = {.}, address = {.}, edition = {.}, note = {accepted for publishing, to appear in 2014 }, } |

Bienert,; Richter,; Stelling,; Maas, 3D-Vegetationsmodell aus Laserscannerdaten für forstmeteorologische Anwendungen am Beispiel des TurbEFA-Projektes (Vortrag) @presentation{Bienert2014, name = {3D-Vegetationsmodell aus Laserscannerdaten für forstmeteorologische Anwendungen am Beispiel des TurbEFA-Projektes}, author = {Bienert, A. and Richter, K. and Stelling, N. and Maas, H.-G}, year = {2014}, date = {2014-12-02}, abstract = {3D-Vegetationsmodelle sind in der Forstmeteorologie ein essentieller Bestandteil um Modellierungen durchzuführen und Messmethoden zu validieren. Inhomogenitäten, wie Änderungen der Bestandshöhe und Lichtungen in Waldbeständen, beeinflussen die Entstehung und die Struktur von turbulenten Windfeldern. Auch die numerische Simulation hochturbulenter Strömungen erfordert eine enorme Rechenleistung unter Verwendung von Vegetationsdaten. Daher ist die Anwendung von Vegetationsmodellen unterschiedlicher Art dringend notwendig. Während bisher die Verteilung der Biomasse von Untersuchungsgebieten über herkömmliche Methoden (Forstinventur, Abgriff aus Forstkarten) erfasst wurde, ist das Flugzeuglaserscanning (ALS) sowie das terrestrische Laserscanning (TLS) ein interessantes Werkzeug zur detaillierten Vegetationserfassung (Maas, 2010). Der Beitrag gibt einen Überblick über die Möglichkeiten der Generierung von Vegetationsmodellen aus verschiedenen Laserscannerdaten. Während Flugzeuglaserscanner große Gebiete aus der Luft erfassen können, sind die terrestrischen Laserscanner aufgrund der bodennahen Standpunkte auf kleinere Gebiete begrenzt. ALS- und TLS-Datensätze sind insofern komplementär, als Flugzeuglaserscannerdaten primär Kronenbereiche erfassen, während TLS-Aufnahmen hochaufgelöste Informationen über Baumstämme und den unteren Kronenbereich liefern. Eine vergleichsweise neue Messmethode im ALS ist das Full- Waveform Laserscanning, bei der das gesamte Intensitätssignal der reflektierten Energie aufgezeichnet und digitalisiert wird. Dadurch ist eine Volumenrekonstruktion der vertikalen Bestandsschicht möglich. Das Verfahren zeigt höhere Genauigkeiten hinsichtlich der Biomasseabschätzung im Vergleich zu dem herkömmlichen Flugzeuglaserscanning. Die unorganisierten 3D-Punktwolken, wie sie beim terrestrischen und Flugzeuglaserscanning entstehen, sind in der Regel für numerische Simulationen nicht handhabbar. Durch geeignete 3D-Datenstrukturen werden Gitterstrukturen auf Basis der Punktwolken aufgebaut und für numerische Simulationsprozesse nutzbar gemacht. Durch die Projektion der Full-Waveform Flugzeuglaserscannerdaten in diese Datenstruktur ergibt sich eine Voxelraumrepräsentation eines Waldbestandes. Hochaufgelöste TLS-Vegetationsscans ermöglichen eine detailliertere Parametrisierung der Pflanzenarchitektur. Über statistische und punktverteilungsbeschreibende Parameter aus den Punkten einer Gitterzelle können u.a. Informationen über Pflanzenflächendichte-Verteilungen (PAD) abgeleitet werden. Die standpunktweise Reflexionswahrscheinlichkeit pro Voxel wird mit Ray-Tracing Methoden bestimmt und repräsentiert den PAD (Queck et., 2012). Die Verwendung dieser Daten zielt auf eine genauere Modellierung der Strömungseffekte an Waldrandkanten, als natürliche Inhomogenität, ab, welche Forschungsschwerpunkt des interdisziplinären Projektes TurbEFA (Turbulent Exchange processes between Forested areas and the Atmosphere) ist.}, } 3D-Vegetationsmodelle sind in der Forstmeteorologie ein essentieller Bestandteil um Modellierungen durchzuführen und Messmethoden zu validieren. Inhomogenitäten, wie Änderungen der Bestandshöhe und Lichtungen in Waldbeständen, beeinflussen die Entstehung und die Struktur von turbulenten Windfeldern. Auch die numerische Simulation hochturbulenter Strömungen erfordert eine enorme Rechenleistung unter Verwendung von Vegetationsdaten. Daher ist die Anwendung von Vegetationsmodellen unterschiedlicher Art dringend notwendig. Während bisher die Verteilung der Biomasse von Untersuchungsgebieten über herkömmliche Methoden (Forstinventur, Abgriff aus Forstkarten) erfasst wurde, ist das Flugzeuglaserscanning (ALS) sowie das terrestrische Laserscanning (TLS) ein interessantes Werkzeug zur detaillierten Vegetationserfassung (Maas, 2010). Der Beitrag gibt einen Überblick über die Möglichkeiten der Generierung von Vegetationsmodellen aus verschiedenen Laserscannerdaten. Während Flugzeuglaserscanner große Gebiete aus der Luft erfassen können, sind die terrestrischen Laserscanner aufgrund der bodennahen Standpunkte auf kleinere Gebiete begrenzt. ALS- und TLS-Datensätze sind insofern komplementär, als Flugzeuglaserscannerdaten primär Kronenbereiche erfassen, während TLS-Aufnahmen hochaufgelöste Informationen über Baumstämme und den unteren Kronenbereich liefern. Eine vergleichsweise neue Messmethode im ALS ist das Full- Waveform Laserscanning, bei der das gesamte Intensitätssignal der reflektierten Energie aufgezeichnet und digitalisiert wird. Dadurch ist eine Volumenrekonstruktion der vertikalen Bestandsschicht möglich. Das Verfahren zeigt höhere Genauigkeiten hinsichtlich der Biomasseabschätzung im Vergleich zu dem herkömmlichen Flugzeuglaserscanning. Die unorganisierten 3D-Punktwolken, wie sie beim terrestrischen und Flugzeuglaserscanning entstehen, sind in der Regel für numerische Simulationen nicht handhabbar. Durch geeignete 3D-Datenstrukturen werden Gitterstrukturen auf Basis der Punktwolken aufgebaut und für numerische Simulationsprozesse nutzbar gemacht. Durch die Projektion der Full-Waveform Flugzeuglaserscannerdaten in diese Datenstruktur ergibt sich eine Voxelraumrepräsentation eines Waldbestandes. Hochaufgelöste TLS-Vegetationsscans ermöglichen eine detailliertere Parametrisierung der Pflanzenarchitektur. Über statistische und punktverteilungsbeschreibende Parameter aus den Punkten einer Gitterzelle können u.a. Informationen über Pflanzenflächendichte-Verteilungen (PAD) abgeleitet werden. Die standpunktweise Reflexionswahrscheinlichkeit pro Voxel wird mit Ray-Tracing Methoden bestimmt und repräsentiert den PAD (Queck et., 2012). Die Verwendung dieser Daten zielt auf eine genauere Modellierung der Strömungseffekte an Waldrandkanten, als natürliche Inhomogenität, ab, welche Forschungsschwerpunkt des interdisziplinären Projektes TurbEFA (Turbulent Exchange processes between Forested areas and the Atmosphere) ist. |

Ziemer,; Wacker, A Comparative Study of B , Γ and Log Normal Distributions in a Three Moment Parameterization for Drop Sedimentation (Artikel) Atmosphere, 5, 3, Seite(n): 484-517, 2014. @article{Ziemer2015, name = {A Comparative Study of B , Γ and Log Normal Distributions in a Three Moment Parameterization for Drop Sedimentation}, author = {Ziemer, C. and Wacker, U.}, year = {2014}, date = {2014-04-01}, journal = {Atmosphere}, volume = {5}, number = {3}, pages = {484-517}, abstract = {This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes.}, } This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes. |

von Larcher T., Beck Klein Horenko Metzner Ph. Waidmann Igdalov Gassner Munz A Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation (Artikel) Meteorologische Zeitschrift, 2014. (BibTeX) @article{vonLarcher2014, name = {A Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation}, author = {von Larcher, T., Beck, A., Klein, R., Horenko, I., Metzner, Ph., Waidmann, M., Igdalov, D., Gassner, G., Munz , C.-D. }, note = {submitted}, year = {2014}, date = {2014-01-28}, journal = {Meteorologische Zeitschrift}, note = {submitted}, } |

Metzner, Ph.; Waidmann,; Igdalov,; von Larcher,; Horenko,; Klein,; Beck,; Gassner, A stochastic closure approach for LES with application to turbulent channel flow. Direct and Large-Eddy Simulation IX (Artikel) 2014. (BibTeX) @article{Metzner2014, name = {A stochastic closure approach for LES with application to turbulent channel flow. Direct and Large-Eddy Simulation IX}, author = {Metzner, Ph. and Waidmann, M. and Igdalov, D. and von Larcher, T. and Horenko, I. and Klein, R. and Beck, A. and Gassner, G.}, note = {Submitted}, year = {2014}, date = {2014-03-20}, note = {Submitted}, } |

Yelash,; Müller,; Lukacova-Medvidova,; Giraldo,; Wirth, Adaptive discontinuous evolution Galerkin method for dry atmospheric flow (Artikel) Journal of Computational Physics, 268, Seite(n): 106 -133, 2014. @article{Yelash2014, name = {Adaptive discontinuous evolution Galerkin method for dry atmospheric flow}, author = {Yelash, L. and Müller, A. and Lukacova-Medvidova, M. and Giraldo, F.X. and Wirth, V.}, url = {http://www.sciencedirect.com/science/article/pii/S002199911400}, year = {2014}, date = {2014-04-07}, journal = {Journal of Computational Physics}, volume = {268}, pages = {106 -133}, abstract = {We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows, nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realized by the IMEX type approximation using the semi-implicit second-order backward differentiation formula (BDF2). Moreover in order to approximate efficiently small scale phenomena, adaptive mesh refinement using the space filling curves via the AMATOS function library is employed. Four standard meteorological test cases are used to validate the new discontinuous evolution Galerkin method for dry atmospheric convection. Comparisons with the Rusanov flux, a standard one-dimensional approximate Riemann solver used for the flux integration, demonstrate better stability and accuracy, as well as the reliability of the new multidimensional DEG method.}, } We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows, nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realized by the IMEX type approximation using the semi-implicit second-order backward differentiation formula (BDF2). Moreover in order to approximate efficiently small scale phenomena, adaptive mesh refinement using the space filling curves via the AMATOS function library is employed. Four standard meteorological test cases are used to validate the new discontinuous evolution Galerkin method for dry atmospheric convection. Comparisons with the Rusanov flux, a standard one-dimensional approximate Riemann solver used for the flux integration, demonstrate better stability and accuracy, as well as the reliability of the new multidimensional DEG method. |

von Vincze M., Harlander Larcher Egbers An experimental study of regime transitions in a differentially heated baroclinic annulus with flat and sloping bottom topographies (Artikel) Nonlinear Processes in Geophysics, Manuscript No.: npg-2013-110, 2014. @article{Vincze2014, name = {An experimental study of regime transitions in a differentially heated baroclinic annulus with flat and sloping bottom topographies}, author = {Vincze, M., Harlander, U., von Larcher, T., Egbers, C.}, note = {accepted}, url = {http://arxiv.org/abs/1309.0321}, year = {2014}, date = {2014-01-06}, journal = {Nonlinear Processes in Geophysics}, volume = {Manuscript No.: npg-2013-110}, abstract = {A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been identified and their phase boundaries -- expressed in terms of appropriate non-dimensional parameters -- have been compared to the recent numerical results of \citet{thomas_slope}. In the flat bottom case, the numerically predicted alignment of the boundary between the axisymmetric and the regular wave flow regime was found to be consistent with the experimental results. However, once the sloping bottom end wall was introduced, the detected behaviour was qualitatively different from that of the simulations. This disagreement is thought to be the consequence of nonlinear wave-wave interactions that could not be resolved in the framework of the numerical study. This argument is supported by the observed development of interference vacillation in the runs with sloping bottom, a mixed flow state in which baroclinic wave modes exhibiting different drift rates and amplitudes can co-exist. }, note = {accepted}, } A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been identified and their phase boundaries -- expressed in terms of appropriate non-dimensional parameters -- have been compared to the recent numerical results of \citet{thomas_slope}. In the flat bottom case, the numerically predicted alignment of the boundary between the axisymmetric and the regular wave flow regime was found to be consistent with the experimental results. However, once the sloping bottom end wall was introduced, the detected behaviour was qualitatively different from that of the simulations. This disagreement is thought to be the consequence of nonlinear wave-wave interactions that could not be resolved in the framework of the numerical study. This argument is supported by the observed development of interference vacillation in the runs with sloping bottom, a mixed flow state in which baroclinic wave modes exhibiting different drift rates and amplitudes can co-exist. |

von M. Vincze S. Borchert, Achatz Th. Larcher Baumann Hertel Remmler Beck Alexandrov Egbers Fröhlich Heuveline Hickel; Harlander, Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics (Artikel) Meteorologische Zeitschrift, 2014. @article{Vincze2014, name = {Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics}, author = {M. Vincze, S. Borchert, U. Achatz, Th. von Larcher, M. Baumann, C. Hertel, S. Remmler, T. Beck, K. Alexandrov, C. Egbers, J. Fröhlich, V. Heuveline, S. Hickel, and U. Harlander}, note = {Submitted}, url = {http://arxiv.org/abs/1403.2715}, year = {2014}, date = {2014-03-19}, journal = {Meteorologische Zeitschrift}, abstract = {The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain "benchmarks" have been created that can later be used as test cases for atmospheric numerical model validation. }, note = {Submitted}, } The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain "benchmarks" have been created that can later be used as test cases for atmospheric numerical model validation. |

C. Ziemer, Wacker Editor View of Item: A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation (Artikel) Atmosphere, 5, 3, Seite(n): 484-517, 2014, ISBN: 2073-4433. @article{Ziemer2014, name = {Editor View of Item: A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation}, author = {C. Ziemer, U. Wacker}, url = {10.3390/atmos5030484 http://www.mdpi.com/2073-4433/5/3/484}, isbn = {2073-4433}, year = {2014}, date = {2014-07-24}, journal = {Atmosphere}, volume = {5}, number = {3}, pages = {484-517}, abstract = {This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes. }, } This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes. |

Siewert,; Bordás,; Wacker,; Beheng,; Kunnen,; Meinke,; Schröder,; Thévenin, Influence of turbulence on the drop growth in warm clouds, Part I: comparison of numerically and experimentally determined collision kernels (Artikel) Meteorologische Zeitschrift, 23, 4, Seite(n): 397 -410, 2014. @article{Siewert2015, name = {Influence of turbulence on the drop growth in warm clouds, Part I: comparison of numerically and experimentally determined collision kernels}, author = {Siewert, C. and Bordás, R. and Wacker, U. and Beheng, K.D. and Kunnen, R. P. J. and Meinke, M. and Schröder, W. and Thévenin, D.}, url = {http://www.schweizerbart.de/papers/metz/detail/23/84311/Influence_of_turbulence_on_the_drop_growth_in_warm_clouds_Part_I_comparison_of_numerically_and_experimentally_determined_collision_kernels?l=DE}, year = {2014}, date = {2014-04-01}, journal = {Meteorologische Zeitschrift}, volume = {23}, number = {4}, pages = {397 -410}, abstract = {This study deals with the comparison of numerically and experimentally determined collision kernels of water drops in air turbulence. The numerical and experimental setups are matched as closely as possible. However, due to the individual numerical and experimental restrictions, it could not be avoided that the turbulent kinetic energy dissipation rate of the measurement and the simulations differ. Direct numerical simulations (DNS) are performed resulting in a very large database concerning geometric collision kernels with 1470 individual entries. Based on this database a fit function for the turbulent enhancement of the collision kernel is developed. In the experiments, the collision rates of large drops (radius > 7.5μm$> 7.5\,\text{\textmu{}m}$) are measured. These collision rates are compared with the developed fit, evaluated at the measurement conditions. Since the total collision rates match well for all occurring dissipation rates the distribution information of the fit could be used to enhance the statistical reliability and for the first time an experimental collision kernel could be constructed. In addition to the collision rates, the drop size distributions at three consecutive streamwise positions are measured. The drop size distributions contain mainly small drops (radius < 7.5μm$< 7.5\,\text{\textmu{}m}$). The measured evolution of the drop size distribution is confronted with model calculations based on the newly derived fit of the collision kernel. It turns out that the observed fast evolution of the drop size distribution can only be modeled if the collision kernel for small drops is drastically increased. A physical argument for this amplification is missing since for such small drops, neither DNSs nor experiments have been performed. For large drops, for which a good agreement of the collision rates was found in the DNS and the experiment, the time for the evolution of the spectrum in the wind tunnel is too short to draw any conclusion. Hence, the long-time evolution of the drop size distribution is presented in a submitted paper by Riechelmann et al. }, } This study deals with the comparison of numerically and experimentally determined collision kernels of water drops in air turbulence. The numerical and experimental setups are matched as closely as possible. However, due to the individual numerical and experimental restrictions, it could not be avoided that the turbulent kinetic energy dissipation rate of the measurement and the simulations differ. Direct numerical simulations (DNS) are performed resulting in a very large database concerning geometric collision kernels with 1470 individual entries. Based on this database a fit function for the turbulent enhancement of the collision kernel is developed. In the experiments, the collision rates of large drops (radius > 7.5μm$> 7.5\,\text{\textmu{}m}$) are measured. These collision rates are compared with the developed fit, evaluated at the measurement conditions. Since the total collision rates match well for all occurring dissipation rates the distribution information of the fit could be used to enhance the statistical reliability and for the first time an experimental collision kernel could be constructed. In addition to the collision rates, the drop size distributions at three consecutive streamwise positions are measured. The drop size distributions contain mainly small drops (radius < 7.5μm$< 7.5\,\text{\textmu{}m}$). The measured evolution of the drop size distribution is confronted with model calculations based on the newly derived fit of the collision kernel. It turns out that the observed fast evolution of the drop size distribution can only be modeled if the collision kernel for small drops is drastically increased. A physical argument for this amplification is missing since for such small drops, neither DNSs nor experiments have been performed. For large drops, for which a good agreement of the collision rates was found in the DNS and the experiment, the time for the evolution of the spectrum in the wind tunnel is too short to draw any conclusion. Hence, the long-time evolution of the drop size distribution is presented in a submitted paper by Riechelmann et al. |

von Larcher T., Dörnbrack Numerical simulations of baroclinic driven flows in a thermally driven rotating annulus using the immersed boundary method (Artikel) Meteorologische Zeitschrift, 2014. (BibTeX) @article{Larcher2014, name = {Numerical simulations of baroclinic driven flows in a thermally driven rotating annulus using the immersed boundary method}, author = {von Larcher, T., Dörnbrack, A.}, note = {to appear}, year = {2014}, date = {2014-11-20}, journal = {Meteorologische Zeitschrift}, note = {to appear}, } |

Muraschko J., Fruman Achatz Hickel Toledo On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves (Artikel) Quarterly Journal of the Royal Meteorological Society, 2014. @article{Muraschko2014, name = {On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves}, author = {Muraschko, J., Fruman, M.D., Achatz, U., Hickel, S., Toledo, Y.}, url = {10.1002/qj.2381 http://onlinelibrary.wiley.com/doi/10.1002/qj.2381/references}, year = {2014}, date = {2014-06-02}, journal = {Quarterly Journal of the Royal Meteorological Society}, abstract = {The dynamics of internal gravity waves is modelled using WKB theory in position-wavenumber phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and timedependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problemthat occurs inWKB ray-tracingmodels when the wavenumber becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volumemethod, and a Lagrangian “phase-space ray tracer” that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wavenumber. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet, and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parameterizations of atmospheric gravity waves in weather and climate models.}, } The dynamics of internal gravity waves is modelled using WKB theory in position-wavenumber phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and timedependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problemthat occurs inWKB ray-tracingmodels when the wavenumber becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volumemethod, and a Lagrangian “phase-space ray tracer” that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wavenumber. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet, and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parameterizations of atmospheric gravity waves in weather and climate models. |

Ziemer,; Jasor,; Wacker,; Beheng,; Polifke, Quantitative comparison of presumed number density and quadrature moment methods for the parameterisation of drop sedimentation (Artikel) Meteorologische Zeitschrift, 23, 4, Seite(n): 411-423, 2014. @article{Ziemer2015, name = {Quantitative comparison of presumed number density and quadrature moment methods for the parameterisation of drop sedimentation}, author = {Ziemer, C. and Jasor, G. and Wacker, U. and Beheng, K.D. and Polifke, W.}, url = {http://www.schweizerbart.de/papers/metz/detail/23/84311/Influence_of_turbulence_on_the_drop_growth_in_warm_clouds_Part_I_comparison_of_numerically_and_experimentally_determined_collision_kernels?l=DE}, year = {2014}, date = {2014-04-01}, journal = {Meteorologische Zeitschrift}, volume = {23}, number = {4}, pages = {411-423}, abstract = {In numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integration limit and a quadrature method, are applied to a one-dimensional test case (‘rainshaft’) for drop sedimentation. The results are compared with those of a reference spectral model. An error norm is introduced, which is based on several characteristic properties of the drop ensemble relevant to the cloud microphysics context. This error norm makes it possible to carry out a quantitative comparison between the two methods. It turns out that the two moment methods presented constitute an improvement regarding two-moment presumed-number-density-function methods from literature for a variety of initial conditions. However, they are excelled by a traditional three-moment presumed-number-density-function method which requires less computational effort. Comparisons of error scores and moment profiles reveal that error scores alone should not be taken for a comparison of parameterisations, since moment profile characteristics can be lost in the integral value of the error norm.}, } In numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integration limit and a quadrature method, are applied to a one-dimensional test case (‘rainshaft’) for drop sedimentation. The results are compared with those of a reference spectral model. An error norm is introduced, which is based on several characteristic properties of the drop ensemble relevant to the cloud microphysics context. This error norm makes it possible to carry out a quantitative comparison between the two methods. It turns out that the two moment methods presented constitute an improvement regarding two-moment presumed-number-density-function methods from literature for a variety of initial conditions. However, they are excelled by a traditional three-moment presumed-number-density-function method which requires less computational effort. Comparisons of error scores and moment profiles reveal that error scores alone should not be taken for a comparison of parameterisations, since moment profile characteristics can be lost in the integral value of the error norm. |

Bauer W., Baumann Scheck Gassmann Heuveline Jones Simulation of tropical-cyclone-like vortices in shallow-water ICON-hex using goal-oriented r-adaptivity (Artikel) Theoretical and Computational Fluid Dynamics, 28, 1, Seite(n): 107-128, 2014, ISSN: Print: 0935-4964; Online: 1432-2250. @article{Bauer2014, name = {Simulation of tropical-cyclone-like vortices in shallow-water ICON-hex using goal-oriented r-adaptivity}, author = {Bauer, W., Baumann, M., Scheck, L., Gassmann, A., Heuveline, V., Jones, S.C.}, note = {10.1007/s00162-013-0303-4}, url = {http://link.springer.com/article/10.1007%2Fs00162-013-0303-4}, issn = {Print: 0935-4964; Online: 1432-2250}, year = {2014}, date = {2014-01-02}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {28}, number = {1}, pages = {107-128}, abstract = {We demonstrate how efficient r-adapted grids for the prediction of tropical cyclone (TC) tracks can be constructed with the help of goal-oriented error estimates. The binary interaction of TCs in a barotropic model is used as a test case. We perform a linear sensitivity analysis for this problem to evaluate the contribution of each grid cell to an error measure correlated with the cyclone positions. This information allows us to estimate the local grid resolution required to minimize the TC position error. An algorithm involving the solution of a Poisson problem is employed to compute how grid points should be moved such that the desired local resolution is achieved. A hexagonal shallow-water version of the next-generation numerical weather prediction and climate model ICON is used to perform model runs on these adapted grids. The results show that for adequately chosen grid adaptation parameters, the accuracy of the track prediction can be maintained even when a coarser grid is used in regions for which the estimated error contribution is low. Accurate track predictions are obtained only when a grid with high resolution consisting of cells with nearly constant size and regular shape covers the part of the domain where the estimated error contribution is large. The number of grid points required to achieve a certain accuracy in the track prediction can be decreased substantially with our approach.}, note = {10.1007/s00162-013-0303-4}, } We demonstrate how efficient r-adapted grids for the prediction of tropical cyclone (TC) tracks can be constructed with the help of goal-oriented error estimates. The binary interaction of TCs in a barotropic model is used as a test case. We perform a linear sensitivity analysis for this problem to evaluate the contribution of each grid cell to an error measure correlated with the cyclone positions. This information allows us to estimate the local grid resolution required to minimize the TC position error. An algorithm involving the solution of a Poisson problem is employed to compute how grid points should be moved such that the desired local resolution is achieved. A hexagonal shallow-water version of the next-generation numerical weather prediction and climate model ICON is used to perform model runs on these adapted grids. The results show that for adequately chosen grid adaptation parameters, the accuracy of the track prediction can be maintained even when a coarser grid is used in regions for which the estimated error contribution is low. Accurate track predictions are obtained only when a grid with high resolution consisting of cells with nearly constant size and regular shape covers the part of the domain where the estimated error contribution is large. The number of grid points required to achieve a certain accuracy in the track prediction can be decreased substantially with our approach. |

Remmler S., Hickel Spectral eddy viscosity of stratified turbulence (Artikel) Journal of Fluid Mechanics, 2014. @article{Remmler 2014, name = {Spectral eddy viscosity of stratified turbulence}, author = {Remmler, S., Hickel, S.}, url = {In press}, year = {2014}, date = {2014-08-29}, journal = {Journal of Fluid Mechanics}, abstract = {ct: Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.}, } ct: Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid. |

Th. von Larcher R. Klein, Horenko Metzner Waidmann Igdalov Beck Gassner; C.-D. Munz, Towards a stochastic closure approach for Large Eddy Simulation (Artikel) in: Finite Volumes for Complex Applications VII, Springer Proceedings in Mathematics and Statistics, 77 and 78, Seite(n): 883-890 , 2014, ISBN: ISBN 978-3-319-06402-4. @article{larcher2014, name = {Towards a stochastic closure approach for Large Eddy Simulation}, author = {Th. von Larcher, R. Klein, I. Horenko, P. Metzner, M. Waidmann, D. Igdalov, A. Beck, G. Gassner, and C.-D. Munz,}, editor = {Fuhrmann, J., Ohlberger, M., Rohde, C.}, url = {10.1007/978-3-319-05591-6_89}, isbn = {ISBN 978-3-319-06402-4}, year = {2014}, date = {2014-03-26}, journal = { in: Finite Volumes for Complex Applications VII, Springer Proceedings in Mathematics and Statistics}, volume = {77 and 78}, pages = {883-890 }, abstract = {We present a stochastic sub grid scale modeling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field that are universally valid for arbitrary control volumes. We model the space-time structure of the fluxes to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory for the model discrimination are used to construct stochastic surrogate models for the non-resolved fluctuations. Vector-valued auto-regressive models with external influences (VARX-models) form the basis for the modeling approach. The reconstruction capabilities of the modeling ansatz are tested against fully three dimensional turbulent channel flow data computed by direct numerical simulation (DNS). We present here the outcome of our reconstruction tests.}, } We present a stochastic sub grid scale modeling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field that are universally valid for arbitrary control volumes. We model the space-time structure of the fluxes to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory for the model discrimination are used to construct stochastic surrogate models for the non-resolved fluctuations. Vector-valued auto-regressive models with external influences (VARX-models) form the basis for the modeling approach. The reconstruction capabilities of the modeling ansatz are tested against fully three dimensional turbulent channel flow data computed by direct numerical simulation (DNS). We present here the outcome of our reconstruction tests. |

Queck,; Bernhofer,; Bienert,; Eipper,; Goldberg,; Harmansa,; Hildebrand,; Maas,; Schlegel,; Stiller, TurbEFA: an interdisciplinary effort to investigate the turbulent flow across a forest clearing (Artikel) Meteorologische Zeitschrift, 1, 2014. @article{Queck2015, name = {TurbEFA: an interdisciplinary effort to investigate the turbulent flow across a forest clearing}, author = {Queck, R. and Bernhofer, C. and Bienert, A. and Eipper, T. and Goldberg, V. and Harmansa, S. and Hildebrand, V. and Maas, H.-G and Schlegel, F. and Stiller, J.}, year = {2014}, date = {2014-07-25}, journal = {Meteorologische Zeitschrift}, volume = {1}, abstract = {the atmosphere within turbulence closure models is mainly limited by a realistic three-dimensional (3D) representation of the vegetation architecture. Within this contribution we present a method to record the 3D vegetation structure and to use this information to derive model parameters that are suitable for numerical flow models. A mixed conifer forest stand around a clearing was scanned and represented by a dense 3D point cloud applying a terrestrial laser scanner. Thus, the plant area density (PAD) with a resolution of one cubic meter was provided for analysis and for numerical simulations. Multi-level high-frequency wind velocity measurements were recorded simultaneously by 27 ultrasonic anemometers on 4 towers for a period of one year. The relationship between wind speed, Reynolds stress and PAD was investigated and a parametrization of the drag coefficient CD by the PAD is suggested. The derived 3D vegetation model and a simpler model (based on classical forest assessments of the site) were applied in a boundary layer model (BLM) and in large-eddy simulations (LES). The spatial development of the turbulent flow over the clearing is further demonstrated by the results of a wind tunnel experiment. The project showed, that the simulation results were improved significantly by the usage of realistic vegetation models. 3D simulations are necessary to depict the influence of heterogeneous canopies on the turbulent flow. Whereas we found limits for the mapping of the vegetation structure within the wind tunnel, there is a considerable potential for numerical simulations. The field measurements and the LES gave new insight into the turbulent flow in the vicinity and across the clearing. The results show that the zones of intensive turbulence development can not be restricted to the locations found in previous studies with more idealized canopies.}, } the atmosphere within turbulence closure models is mainly limited by a realistic three-dimensional (3D) representation of the vegetation architecture. Within this contribution we present a method to record the 3D vegetation structure and to use this information to derive model parameters that are suitable for numerical flow models. A mixed conifer forest stand around a clearing was scanned and represented by a dense 3D point cloud applying a terrestrial laser scanner. Thus, the plant area density (PAD) with a resolution of one cubic meter was provided for analysis and for numerical simulations. Multi-level high-frequency wind velocity measurements were recorded simultaneously by 27 ultrasonic anemometers on 4 towers for a period of one year. The relationship between wind speed, Reynolds stress and PAD was investigated and a parametrization of the drag coefficient CD by the PAD is suggested. The derived 3D vegetation model and a simpler model (based on classical forest assessments of the site) were applied in a boundary layer model (BLM) and in large-eddy simulations (LES). The spatial development of the turbulent flow over the clearing is further demonstrated by the results of a wind tunnel experiment. The project showed, that the simulation results were improved significantly by the usage of realistic vegetation models. 3D simulations are necessary to depict the influence of heterogeneous canopies on the turbulent flow. Whereas we found limits for the mapping of the vegetation structure within the wind tunnel, there is a considerable potential for numerical simulations. The field measurements and the LES gave new insight into the turbulent flow in the vicinity and across the clearing. The results show that the zones of intensive turbulence development can not be restricted to the locations found in previous studies with more idealized canopies. |

Queck,; Bernhofer,; Goldberg,; Harmansa,; Bienert,; Maas,; Schlegel,; Stiller,; Eipper,; Hildebrand, TurbEFA: Ein interdisziplinärer Ansatz zur Untersuchung der turbulenten Strömung an einer Waldlichtung (Vortrag) @presentation{Queck2014, name = {TurbEFA: Ein interdisziplinärer Ansatz zur Untersuchung der turbulenten Strömung an einer Waldlichtung}, author = {Queck, R. and Bernhofer, C. and Goldberg, V. and Harmansa, S. and Bienert, A. and Maas, H.-G and Schlegel, F. and Stiller, J. and Eipper, T. and Hildebrand, V.}, year = {2014}, date = {2014-12-02}, abstract = {Waldökosysteme spielen eine bedeutende Rolle in der Interaktion zwischen Landoberfläche und Atmosphäre. Ein besseres Verständnis der Austauschprozesse ist unter anderem notwendig für eine Einschätzung der Absorption und Emission von Spurenstoffen (z.B. CO2) und der Risiken von Waldschäden durch Wind, Frost und Dürre. Heutige Studien zur Rolle von terrestrischen Ökosystemen im Wasser- und Kohlenstoffkreislauf basieren auf langfristigen Messungen des Energie- und Massenaustausches zwischen Vegetation und Atmosphäre durch die Eddy-Kovarianz Methode (Goulden et al. 1996). Mehr als 500 Standorte weltweit sind derzeit in FLUXNET organisiert, einem internationalen Netzwerk (Baldocchi et al. 2001) zur kontinuierliche Messungen des Stoff- und Energieaustausches nach standardisierten Methoden (Aubinet et al. 2000). Der Austausch von Waldökosystemen wird dabei an einem Messturm durch eine Punktmessung über dem Bestand bestimmt, die eine bestimmte häufig komplexe Quellfläche repräsentiert. Mehr als drei Dekaden der Forschung in Feldexperimenten und Modellierung haben gezeigt, dass verbleibende Unsicherheiten vor allem durch räumliche Inhomogenität des Austausches begründet sind. Insbesondere fehlen Ansätze für eine geeignete Parametrisierung dieser Inhomogenitäten in numerischen Modellen.}, } Waldökosysteme spielen eine bedeutende Rolle in der Interaktion zwischen Landoberfläche und Atmosphäre. Ein besseres Verständnis der Austauschprozesse ist unter anderem notwendig für eine Einschätzung der Absorption und Emission von Spurenstoffen (z.B. CO2) und der Risiken von Waldschäden durch Wind, Frost und Dürre. Heutige Studien zur Rolle von terrestrischen Ökosystemen im Wasser- und Kohlenstoffkreislauf basieren auf langfristigen Messungen des Energie- und Massenaustausches zwischen Vegetation und Atmosphäre durch die Eddy-Kovarianz Methode (Goulden et al. 1996). Mehr als 500 Standorte weltweit sind derzeit in FLUXNET organisiert, einem internationalen Netzwerk (Baldocchi et al. 2001) zur kontinuierliche Messungen des Stoff- und Energieaustausches nach standardisierten Methoden (Aubinet et al. 2000). Der Austausch von Waldökosystemen wird dabei an einem Messturm durch eine Punktmessung über dem Bestand bestimmt, die eine bestimmte häufig komplexe Quellfläche repräsentiert. Mehr als drei Dekaden der Forschung in Feldexperimenten und Modellierung haben gezeigt, dass verbleibende Unsicherheiten vor allem durch räumliche Inhomogenität des Austausches begründet sind. Insbesondere fehlen Ansätze für eine geeignete Parametrisierung dieser Inhomogenitäten in numerischen Modellen. |

## 2013 |

Benacchio T., O'Neill; Klein, A blended soundproof-to-compressible numerical model for atmospheric dynamics (Artikel) Monthly Weather Review, 2013. @article{Benacchio2013, name = {A blended soundproof-to-compressible numerical model for atmospheric dynamics}, author = {Benacchio, T., O'Neill, W.P. and Klein, R.}, note = {Submitted}, year = {2013}, date = {2013-11-26}, journal = {Monthly Weather Review}, abstract = {A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo-incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown.}, note = {Submitted}, } A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo-incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown. |

Rieper F., Hickel Achatz A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization (Artikel) Monthly Weather Review, 141, 3, Seite(n): 861–886, 2013, ISSN: Online: 1520-0493; Print: 0027-0644 . @article{Rieper2013, name = {A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization}, author = {Rieper, F., Hickel, S., Achatz, U.}, url = {http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-12-00026.1 10.1175/MWR-D-12-00026.1}, issn = {Online: 1520-0493; Print: 0027-0644 }, year = {2013}, date = {2013-03-05}, journal = { Monthly Weather Review}, volume = {141}, number = {3}, pages = {861–886}, abstract = {Durran’s pseudo-incompressible equations are integrated in a mass and momentum conserving way with a new implicit turbulence model. This system is soundproof, which has two major advantages over fully compressible systems: the Courant–Friedrichs–Lewy (CFL) condition for stable time advancement is no longer dictated by the speed of sound and all waves in the model are clearly gravity waves (GW). Thus, the pseudo-incompressible equations are an ideal laboratory model for studying GW generation, propagation, and breaking. Gravity wave breaking creates turbulence that needs to be parameterized. For the first time the adaptive local deconvolution method (ALDM) for implicit large-eddy simulation (ILES) is applied to non-Boussinesq stratified flows. ALDM provides a turbulence model that is fully merged with the discretization of the flux function. In the context of non-Boussinesq stratified flows this poses some new numerical challenges—the solution of which is presented in this text. In numerical test cases the authors show the agreement of the results with the literature (Robert’s hot–cold bubble test case), they present the sensitivity to the model’s resolution and discretization, and they demonstrate qualitatively the behavior of the implicit turbulence model for a 2D breaking gravity wave packet.}, } Durran’s pseudo-incompressible equations are integrated in a mass and momentum conserving way with a new implicit turbulence model. This system is soundproof, which has two major advantages over fully compressible systems: the Courant–Friedrichs–Lewy (CFL) condition for stable time advancement is no longer dictated by the speed of sound and all waves in the model are clearly gravity waves (GW). Thus, the pseudo-incompressible equations are an ideal laboratory model for studying GW generation, propagation, and breaking. Gravity wave breaking creates turbulence that needs to be parameterized. For the first time the adaptive local deconvolution method (ALDM) for implicit large-eddy simulation (ILES) is applied to non-Boussinesq stratified flows. ALDM provides a turbulence model that is fully merged with the discretization of the flux function. In the context of non-Boussinesq stratified flows this poses some new numerical challenges—the solution of which is presented in this text. In numerical test cases the authors show the agreement of the results with the literature (Robert’s hot–cold bubble test case), they present the sensitivity to the model’s resolution and discretization, and they demonstrate qualitatively the behavior of the implicit turbulence model for a 2D breaking gravity wave packet. |

Kanda M., Inagaki Miyamoto Gryschka; Raasch, A New Aerodynamic Parameterization for Real Urban Surfaces (Artikel) Boundary-Layer Meteorology, 148, Seite(n): 357-377, 2013. @article{Kanda2013, name = {A New Aerodynamic Parameterization for Real Urban Surfaces}, author = {Kanda, M., Inagaki, A., Miyamoto, T., Gryschka, M. and Raasch, S.}, url = {http://link.springer.com/article/10.1007%2Fs10546-013-9818-x#page-1}, year = {2013}, date = {2013-02-22}, journal = {Boundary-Layer Meteorology}, volume = {148}, pages = {357-377}, abstract = {This study conducted large-eddy simulations (LES) of fully developed turbulent flow within and above explicitly resolved buildings in Tokyo and Nagoya, Japan. The more than 100 LES results, each covering a 1,000 × 1,000 m2 area with 2-m resolution, provide a database of the horizontally-averaged turbulent statistics and surface drag corresponding to various urban morphologies. The vertical profiles of horizontally-averaged wind velocity mostly follow a logarithmic law even for districts with high-rise buildings, allowing estimates of aerodynamic parameters such as displacement height and roughness length using the von Karman constant = 0.4. As an alternative derivation of the aerodynamic parameters, a regression of roughness length and variable Karman constant was also attempted, using a displacement height physically determined as the central height of drag action. Although both the regression methods worked, the former gives larger (smaller) values of displacement height (roughness length) by 20–25%than the latter. The LES database clearly illustrates the essential difference in bulk flow properties between real urban surfaces and simplified arrays. The vertical profiles of horizontally-averaged momentum flux were influenced by the maximum building height and the standard deviation of building height, as well as conventional geometric parameters such as the average building height, frontal area index, and plane area index. On the basis of these investigations, a new aerodynamic parametrization of roughness length and displacement height in terms of the five geometric parameters described abovewas empirically proposed. The new parametrizations work well for both real urban morphologies and simplified model geometries.}, } This study conducted large-eddy simulations (LES) of fully developed turbulent flow within and above explicitly resolved buildings in Tokyo and Nagoya, Japan. The more than 100 LES results, each covering a 1,000 × 1,000 m2 area with 2-m resolution, provide a database of the horizontally-averaged turbulent statistics and surface drag corresponding to various urban morphologies. The vertical profiles of horizontally-averaged wind velocity mostly follow a logarithmic law even for districts with high-rise buildings, allowing estimates of aerodynamic parameters such as displacement height and roughness length using the von Karman constant = 0.4. As an alternative derivation of the aerodynamic parameters, a regression of roughness length and variable Karman constant was also attempted, using a displacement height physically determined as the central height of drag action. Although both the regression methods worked, the former gives larger (smaller) values of displacement height (roughness length) by 20–25%than the latter. The LES database clearly illustrates the essential difference in bulk flow properties between real urban surfaces and simplified arrays. The vertical profiles of horizontally-averaged momentum flux were influenced by the maximum building height and the standard deviation of building height, as well as conventional geometric parameters such as the average building height, frontal area index, and plane area index. On the basis of these investigations, a new aerodynamic parametrization of roughness length and displacement height in terms of the five geometric parameters described abovewas empirically proposed. The new parametrizations work well for both real urban morphologies and simplified model geometries. |

A. Kacimi, Khouider A numerical investigation of the barotropic instability on the equatorial β-plane (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 491-512, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Kacimi2013, name = {A numerical investigation of the barotropic instability on the equatorial β-plane}, author = {A. Kacimi, B. Khouider }, url = {http://link.springer.com/article/10.1007/s00162-012-0260-3}, issn = { 0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {491-512}, abstract = {The barotropic instability of horizontal shear flows is investigated by using two numerical algorithms to solve the equatorial β-plane barotropic equations. The first is the Arakawa Jacobian method (Arakawa, in J Comput Phys 1:119–143, 1966), which is a second-order-centered finite differences scheme that conserves energy and enstrophy, and the second is the fourth-order essentially non-oscillatory scheme for non-linear PDE’s of Osher and Shu (SIAM J Numer Anal 28:907–922, 1991), which is designed to track sharp fronts. We are interested in the performance of these two methods in tracking the long-time behavior of the instability, under the influence of the non-linearity, in the simple case of a Helmholtz shear layer. The associated linear problem is solved analytically, and the linear solution is used as an initial condition for the numerical simulations. We run a series of numerical simulations using both methods with various grid refinements and with two different amplitudes of the initial perturbation. A small viscosity term is added to the vorticity equation to damp the grid-scale waves for Arakawa’s method. This is not necessary for the high-order ENO-4 scheme, which has its own grid-scale dissipation. At high resolution, the two methods are in good agreement; they yield qualitatively and quantitatively the same solution in the long run: for small disturbances, the total flow stabilizes into a steady-state meridional shear with a smooth profile near the equator, while strong disturbances merge together to form a single large-scale vortex that propagates westward, along the equator, consistent with the African easterly waves and the monsoons trough circulation. At coarse resolution, however, Arakawa’s method seems to be much superior to the fourth-order ENO-4 scheme as it provides solutions that are more consistent with the fine resolution one.}, } The barotropic instability of horizontal shear flows is investigated by using two numerical algorithms to solve the equatorial β-plane barotropic equations. The first is the Arakawa Jacobian method (Arakawa, in J Comput Phys 1:119–143, 1966), which is a second-order-centered finite differences scheme that conserves energy and enstrophy, and the second is the fourth-order essentially non-oscillatory scheme for non-linear PDE’s of Osher and Shu (SIAM J Numer Anal 28:907–922, 1991), which is designed to track sharp fronts. We are interested in the performance of these two methods in tracking the long-time behavior of the instability, under the influence of the non-linearity, in the simple case of a Helmholtz shear layer. The associated linear problem is solved analytically, and the linear solution is used as an initial condition for the numerical simulations. We run a series of numerical simulations using both methods with various grid refinements and with two different amplitudes of the initial perturbation. A small viscosity term is added to the vorticity equation to damp the grid-scale waves for Arakawa’s method. This is not necessary for the high-order ENO-4 scheme, which has its own grid-scale dissipation. At high resolution, the two methods are in good agreement; they yield qualitatively and quantitatively the same solution in the long run: for small disturbances, the total flow stabilizes into a steady-state meridional shear with a smooth profile near the equator, while strong disturbances merge together to form a single large-scale vortex that propagates westward, along the equator, consistent with the African easterly waves and the monsoons trough circulation. At coarse resolution, however, Arakawa’s method seems to be much superior to the fourth-order ENO-4 scheme as it provides solutions that are more consistent with the fine resolution one. |

Baldauf M., Brdar An analytic solution for linear gravity waves in a channel as a test for numerical models using the non-hydrostatic, compressible Euler equations (Artikel) Quarterly Journal of the Royal Meteorological Society, 2013. @article{Baldauf2013, name = {An analytic solution for linear gravity waves in a channel as a test for numerical models using the non-hydrostatic, compressible Euler equations}, author = {Baldauf, M., Brdar, S.}, editor = {Royal Meteorological Society}, url = {http://onlinelibrary.wiley.com/doi/10.1002/qj.2105/full 10.1002/qj.2105}, year = {2013}, date = {2013-01-29}, journal = {Quarterly Journal of the Royal Meteorological Society}, abstract = {A slightly modified version of the idealized test set-up used by Skamarock and Klemp is proposed: the quasi linear two-dimensional expansion of sound and gravity waves in a flat channel induced by a weak warm bubble. For this test case an exact analytic solution of the linearized compressible, non-hydrostatic Euler equations for a shallow atmosphere has been derived. This solution can be used as a benchmark to assess compressible, non-hydrostatic dynamical cores which are the basis for many of today's, and probably most of the future, atmospheric models. Comparisons and convergence studies of two quite differently designed numerical limited-area simulation models, COSMO and DUNE, against this analytic solution are performed.}, } A slightly modified version of the idealized test set-up used by Skamarock and Klemp is proposed: the quasi linear two-dimensional expansion of sound and gravity waves in a flat channel induced by a weak warm bubble. For this test case an exact analytic solution of the linearized compressible, non-hydrostatic Euler equations for a shallow atmosphere has been derived. This solution can be used as a benchmark to assess compressible, non-hydrostatic dynamical cores which are the basis for many of today's, and probably most of the future, atmospheric models. Comparisons and convergence studies of two quite differently designed numerical limited-area simulation models, COSMO and DUNE, against this analytic solution are performed. |

H. Schmidt A. R. Kerstein, Wunsch Nédélec Sayler Analysis and numerical simulation of a laboratory analog of radiatively induced cloud-top entrainment (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 377-395, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Schmidt2013, name = {Analysis and numerical simulation of a laboratory analog of radiatively induced cloud-top entrainment}, author = {H. Schmidt, A. R. Kerstein, S. Wunsch, R. Nédélec, B. J. Sayler }, url = {http://link.springer.com/article/10.1007/s00162-012-0288-4}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {377-395}, abstract = {Numerical simulations using the one-dimensional-turbulence (ODT) model are compared to water-tank measurements emulating convection and entrainment in stratiform clouds driven by cloud-top cooling. Measured dependences of the entrainment rate on Richardson number were numerically reproduced for water trials in which the initial stratification is due to temperature differences. For an additional set of trials where the initial stratification is obtained by adding dextrose to the lower layer of the tank, measured dependences of the entrainment rate on Richardson number were partially reproduced, and importantly, the model also captures the measured sensitivity of entrainment to molecular transport. Additional parameter variations suggest other dependences of the entrainment rate. Analysis suggests possible qualitative differences between laboratory and cloud entrainment behaviors that might be testable using ODT.}, } Numerical simulations using the one-dimensional-turbulence (ODT) model are compared to water-tank measurements emulating convection and entrainment in stratiform clouds driven by cloud-top cooling. Measured dependences of the entrainment rate on Richardson number were numerically reproduced for water trials in which the initial stratification is due to temperature differences. For an additional set of trials where the initial stratification is obtained by adding dextrose to the lower layer of the tank, measured dependences of the entrainment rate on Richardson number were partially reproduced, and importantly, the model also captures the measured sensitivity of entrainment to molecular transport. Additional parameter variations suggest other dependences of the entrainment rate. Analysis suggests possible qualitative differences between laboratory and cloud entrainment behaviors that might be testable using ODT. |

B. Kumar J. Schumacher, Shaw Cloud microphysical effects of turbulent mixing and entrainment (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 361-376, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Kumar2013, name = {Cloud microphysical effects of turbulent mixing and entrainment}, author = {B. Kumar, J. Schumacher, R. A. Shaw }, url = {http://link.springer.com/article/10.1007/s00162-012-0272-z}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {361-376}, abstract = {Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.}, } Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered. |

Müller,; Behrens,; Giraldo,; Wirth, Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments (Artikel) Journal of Computational Physics, 235, Seite(n): 371-393, 2013. @article{Mueller2013, name = {Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments}, author = {Müller, A. and Behrens, J. and Giraldo, F.X. and Wirth, V.}, url = {10.1016/j.jcp.2012.10.038}, year = {2013}, date = {2013-04-08}, journal = {Journal of Computational Physics}, volume = {235}, pages = {371-393}, abstract = {Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a discontinuous Galerkin method. Time integration is done with an IMEX-method and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is tested with three standard test cases. An error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For the rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU-time.}, } Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a discontinuous Galerkin method. Time integration is done with an IMEX-method and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is tested with three standard test cases. An error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For the rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU-time. |

S. Brdar M. Baldauf, Dedner Klöfkorn Comparison of dynamical cores for NWP models: comparison of COSMO and Dune (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 453-472, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Brdar2013, name = {Comparison of dynamical cores for NWP models: comparison of COSMO and Dune}, author = {S. Brdar, M. Baldauf, A. Dedner, R. Klöfkorn }, url = {http://link.springer.com/article/10.1007/s00162-012-0264-z}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {453-472}, abstract = {We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000).}, } We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000). |

S. N. Stechmann A. J. Majda, Skjorshammer Convectively coupled wave–environment interactions (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 513-532, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Stechmann2013, name = {Convectively coupled wave–environment interactions}, author = {S. N. Stechmann, A. J. Majda, D. Skjorshammer }, url = {http://link.springer.com/article/10.1007/s00162-012-0268-8}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = { 513-532}, abstract = {In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW–mean flow interactions that are different from traditional wave–mean flow interactions in many ways. CCW–mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth’s equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow’s vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW–mean flow interactions, also discussed are CCW–water vapor interactions, which form the basis of the Madden–Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.}, } In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW–mean flow interactions that are different from traditional wave–mean flow interactions in many ways. CCW–mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth’s equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow’s vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW–mean flow interactions, also discussed are CCW–water vapor interactions, which form the basis of the Madden–Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values. |

Remmler S., Fruman Hickel Direct numerical simulation of a breaking inertia-gravity wave (Artikel) Journal of Fluid Mechanics, 722, Seite(n): 424-436, 2013. @article{Remmler2014, name = {Direct numerical simulation of a breaking inertia-gravity wave}, author = {Remmler, S., Fruman, M.D., Hickel, S.}, url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8874727&fileId=S0022112013001080 10.1017/jfm.2013.108 }, year = {2013}, date = {2013-05-07}, journal = {Journal of Fluid Mechanics}, volume = {722}, pages = {424-436}, abstract = {We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed. }, } We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed. |

Bordás R., Roloff CH. Thévenin Shaw Experimental determination of droplet collision rates in turbulence (Artikel) New Journal of Physics, 15, 045010 , 2013. @article{Bordas2013, name = {Experimental determination of droplet collision rates in turbulence }, author = {Bordás, R., Roloff, CH.,Thévenin, D.,Shaw, R.A.}, editor = {Deutsche Physikalische Gesellschaft}, url = {http://iopscience.iop.org/1367-2630/15/4/045010}, year = {2013}, date = {2013-04-17}, journal = {New Journal of Physics}, volume = {15}, number = {045010 }, abstract = {Inter-particle collisions in turbulent flows are of central importance for many engineering applications and environmental processes. For instance, collision and coalescence is the mechanism for warm rain initiation in cumulus clouds, a still poorly understood issue. This work presents measurements of droplet–droplet interactions in a laboratory turbulent flow, allowing reproducibility and control over initial and boundary conditions. The measured two-phase flow reproduces conditions relevant to cumulus clouds. The turbulent flow and the droplet size distribution are well characterized, and independently the collision rate is measured. Two independent experimental approaches for determining the collision rate are compared with each other: (i) a high-magnification shadowgraphy setup is employed, applying a deformation threshold as collision indicator. This technique has been specifically adapted to measure droplet collision probability in dispersed two-phase flows. (ii) Corresponding results are compared for the first time with a particle tracking approach, post-processing high-speed shadowgraphy image sequences. Using the measured turbulence and droplet properties, the turbulent collision kernel can be calculated for comparison. The two independent measurements deliver comparable orders of magnitude for the collision probability, highlighting the quality of the measurement process, even if the comparison between both measurement techniques is still associated with a large uncertainty. Comparisons with recently published theoretical predictions show reasonable agreement. The theoretical collision rates accounting for collision efficiency are noticeably closer to the measured values than those accounting only for transport.}, } Inter-particle collisions in turbulent flows are of central importance for many engineering applications and environmental processes. For instance, collision and coalescence is the mechanism for warm rain initiation in cumulus clouds, a still poorly understood issue. This work presents measurements of droplet–droplet interactions in a laboratory turbulent flow, allowing reproducibility and control over initial and boundary conditions. The measured two-phase flow reproduces conditions relevant to cumulus clouds. The turbulent flow and the droplet size distribution are well characterized, and independently the collision rate is measured. Two independent experimental approaches for determining the collision rate are compared with each other: (i) a high-magnification shadowgraphy setup is employed, applying a deformation threshold as collision indicator. This technique has been specifically adapted to measure droplet collision probability in dispersed two-phase flows. (ii) Corresponding results are compared for the first time with a particle tracking approach, post-processing high-speed shadowgraphy image sequences. Using the measured turbulence and droplet properties, the turbulent collision kernel can be calculated for comparison. The two independent measurements deliver comparable orders of magnitude for the collision probability, highlighting the quality of the measurement process, even if the comparison between both measurement techniques is still associated with a large uncertainty. Comparisons with recently published theoretical predictions show reasonable agreement. The theoretical collision rates accounting for collision efficiency are noticeably closer to the measured values than those accounting only for transport. |

M. Braack N. Taschenberger, (To Appear) Hierarchical a posteriori residual based error estimators for bilinear finite elements (Artikel) Int. J. Numer. Anal. Model., 10, 2, Seite(n): 466-480, 2013. (BibTeX) @article{., name = {Hierarchical a posteriori residual based error estimators for bilinear finite elements}, author = {M. Braack, N. Taschenberger, (To Appear)}, year = {2013}, date = {2013-01-01}, journal = {Int. J. Numer. Anal. Model.}, volume = {10}, number = {2}, pages = {466-480}, } |

I. D. Borcia, Harlander Inertial waves in a rotating annulus with inclined inner cylinder: comparing the spectrum of wave attractor frequency bands and the eigenspectrum in the limit of zero inclination (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 397-413, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Borcia2013, name = {Inertial waves in a rotating annulus with inclined inner cylinder: comparing the spectrum of wave attractor frequency bands and the eigenspectrum in the limit of zero inclination}, author = {I. D. Borcia, U. Harlander }, url = {http://link.springer.com/article/10.1007/s00162-012-0278-6}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {397-413}, abstract = {We investigate theoretically inertial waves inside a liquid confined between two co-rotating coaxial cylinders of finite length. We consider the case of small viscosity and high angular velocity (i.e., small Ekman numbers), a parameter range of interest for many geophysical applications. In this case, inertial waves propagating in the container show multiple reflections at the walls before the waves can be damped by weak diffusion. We allow for the inner cylinder wall to be parallel or inclined with respect to the annulus’ vector of rotation (truncated cone). For the limit of zero viscosity, the wave propagation is governed by a boundary value problem that is composed of a linear second-order hyperbolic partial differential equation and the impermeability boundary conditions. For the special case of vertical cylinder walls (no inclination of the inner cylinder), this boundary value problem is separable, the corresponding eigenmodes can analytically be found and they are regular. However, when the inner cylinder wall is inclined, the hyperbolicity of the governing equation leads to internal shear layers (corresponding to singularities for the inviscid case). The geometrical structure of the shear layers can be explained by inertial waves, trapped on limit cycles denoted as wave attractors. The shape of the limit cycles depends on the wave frequency. In fact, the spectrum of regular modes, existing for the case of vertical cylinder walls, vanishes almost completely when the inner wall is inclined. Instead of a spectrum of discrete frequencies and regular eigenmodes, a spectrum of wave attractor frequency bands and singular eigenmodes exist. The question addressed here is whether the spectrum of wave attractor intervals collapses to the discrete frequency spectrum when the inclination angle of the inner cylinder goes to zero. To answer this question, the attractor frequency intervals are evaluated numerically for a series of decreasing cylinder inclination angles and are compared with the analytically found eigenspectrum for the case of zero inclination. Goal is to better understand the asymptotic behavior of the problem for decreasing inclination angles. This understanding helps to interpret results from laboratory experiments with geometries that differ from the perfect annulus with parallel cylinder walls.}, } We investigate theoretically inertial waves inside a liquid confined between two co-rotating coaxial cylinders of finite length. We consider the case of small viscosity and high angular velocity (i.e., small Ekman numbers), a parameter range of interest for many geophysical applications. In this case, inertial waves propagating in the container show multiple reflections at the walls before the waves can be damped by weak diffusion. We allow for the inner cylinder wall to be parallel or inclined with respect to the annulus’ vector of rotation (truncated cone). For the limit of zero viscosity, the wave propagation is governed by a boundary value problem that is composed of a linear second-order hyperbolic partial differential equation and the impermeability boundary conditions. For the special case of vertical cylinder walls (no inclination of the inner cylinder), this boundary value problem is separable, the corresponding eigenmodes can analytically be found and they are regular. However, when the inner cylinder wall is inclined, the hyperbolicity of the governing equation leads to internal shear layers (corresponding to singularities for the inviscid case). The geometrical structure of the shear layers can be explained by inertial waves, trapped on limit cycles denoted as wave attractors. The shape of the limit cycles depends on the wave frequency. In fact, the spectrum of regular modes, existing for the case of vertical cylinder walls, vanishes almost completely when the inner wall is inclined. Instead of a spectrum of discrete frequencies and regular eigenmodes, a spectrum of wave attractor frequency bands and singular eigenmodes exist. The question addressed here is whether the spectrum of wave attractor intervals collapses to the discrete frequency spectrum when the inclination angle of the inner cylinder goes to zero. To answer this question, the attractor frequency intervals are evaluated numerically for a series of decreasing cylinder inclination angles and are compared with the analytically found eigenspectrum for the case of zero inclination. Goal is to better understand the asymptotic behavior of the problem for decreasing inclination angles. This understanding helps to interpret results from laboratory experiments with geometries that differ from the perfect annulus with parallel cylinder walls. |

T. Seelig U. Harlander, Faulwetter Egbers Irregularity and singular vector growth of the differentially heated rotating annulus flow (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 415-432, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Seelig2013, name = {Irregularity and singular vector growth of the differentially heated rotating annulus flow}, author = {T. Seelig, U. Harlander, R. Faulwetter, C. Egbers }, url = {http://link.springer.com/article/10.1007/s00162-011-0255-5}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {415-432}, abstract = {The problem of weather prediction is to a large part determined by the large-scale atmospheric flow. This flow is irregular but not fully turbulent. The irregularity can be related to instability, nonlinear wave–wave interactions, or randomly excited singular vectors. In the present study, the latter mechanism is investigated numerically and experimentally. For this purpose, a baroclinic quasigeostrophic low-order model is adjusted to a differentially heated rotating annulus experiment, an established laboratory analog to the atmospheric circulation. We linearize the low-order model about a time-mean state to study the growth of singular vectors and compare those with singular vectors that have been derived empirically from the experimental data. Qualitative agreement of the numerically and experimentally derived singular vectors form the basis for a deeper analysis of the low-order model. In particular, for a broad range of annulus rotation frequencies and radial temperature differences, we compute the maximal growth rates of the low-order model. These growth rates are displayed as a function of the Taylor and thermal Rossby number, a frame widely used in studies of annulus regime transitions. We can show that most regime transitions defined by E.N. Lorenz in the sixties have their counterpart in the Taylor-Rossby singular value diagram. Most striking is the fact that for the irregular regime by far, the largest growth rates can be found. We suppose that irregularity in the transition region to geostrophic turbulence might for some part result from randomly excited singular vectors with unusual large growth rates. In concert with nonlinear wave–wave coupling, this process might explain the gradual broadening of the wave spectrum that has been found for the route to geostrophic turbulence in annulus flows.}, } The problem of weather prediction is to a large part determined by the large-scale atmospheric flow. This flow is irregular but not fully turbulent. The irregularity can be related to instability, nonlinear wave–wave interactions, or randomly excited singular vectors. In the present study, the latter mechanism is investigated numerically and experimentally. For this purpose, a baroclinic quasigeostrophic low-order model is adjusted to a differentially heated rotating annulus experiment, an established laboratory analog to the atmospheric circulation. We linearize the low-order model about a time-mean state to study the growth of singular vectors and compare those with singular vectors that have been derived empirically from the experimental data. Qualitative agreement of the numerically and experimentally derived singular vectors form the basis for a deeper analysis of the low-order model. In particular, for a broad range of annulus rotation frequencies and radial temperature differences, we compute the maximal growth rates of the low-order model. These growth rates are displayed as a function of the Taylor and thermal Rossby number, a frame widely used in studies of annulus regime transitions. We can show that most regime transitions defined by E.N. Lorenz in the sixties have their counterpart in the Taylor-Rossby singular value diagram. Most striking is the fact that for the irregular regime by far, the largest growth rates can be found. We suppose that irregularity in the transition region to geostrophic turbulence might for some part result from randomly excited singular vectors with unusual large growth rates. In concert with nonlinear wave–wave coupling, this process might explain the gradual broadening of the wave spectrum that has been found for the route to geostrophic turbulence in annulus flows. |

D. O. Lignell A. R. Kerstein, Sun Monson Mesh adaption for efficient multiscale implementation of one-dimensional turbulence (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 273-295, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Lignell2013, name = {Mesh adaption for efficient multiscale implementation of one-dimensional turbulence}, author = {D. O. Lignell, A. R. Kerstein, G. Sun, E. I. Monson }, url = {http://link.springer.com/article/10.1007/s00162-012-0267-9}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {273-295}, abstract = {One-Dimensional Turbulence (ODT) is a stochastic model for turbulent flow simulation. In an atmospheric context, it is analogous to single-column modeling (SCM) in that it lives on a 1D spatial domain, but different in that it time advances individual flow realizations rather than ensemble-averaged quantities. The lack of averaging enables a physically sound multiscale treatment, which is useful for resolving sporadic localized phenomena, as seen in stably stratified regimes, and sharp interfaces, as observed where a convective layer encounters a stable overlying zone. In such flows, the relevant scale range is so large that it is beneficial to enhance model performance by introducing an adaptive mesh. An adaptive-mesh algorithm that provides the desired performance characteristics is described and demonstrated, and its implications for the ODT advancement scheme are explained.}, } One-Dimensional Turbulence (ODT) is a stochastic model for turbulent flow simulation. In an atmospheric context, it is analogous to single-column modeling (SCM) in that it lives on a 1D spatial domain, but different in that it time advances individual flow realizations rather than ensemble-averaged quantities. The lack of averaging enables a physically sound multiscale treatment, which is useful for resolving sporadic localized phenomena, as seen in stably stratified regimes, and sharp interfaces, as observed where a convective layer encounters a stable overlying zone. In such flows, the relevant scale range is so large that it is beneficial to enhance model performance by introducing an adaptive mesh. An adaptive-mesh algorithm that provides the desired performance characteristics is described and demonstrated, and its implications for the ODT advancement scheme are explained. |

R. Bordás V. John, Schmeyer Thévenin Numerical methods for the simulation of a coalescence-driven droplet size distribution (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 253-271, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Bordás2013, name = {Numerical methods for the simulation of a coalescence-driven droplet size distribution}, author = { R. Bordás, V. John, E. Schmeyer, D. Thévenin }, url = {http://link.springer.com/article/10.1007/s00162-012-0275-9}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {253-271}, abstract = {The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.}, } The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed. |

Kunnen,; Siewert,; Meinke,; Schröder,; Beheng, Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds (Artikel) Atmospheric Research, 2013. @article{Kunnen2013, name = {Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds}, author = {R. P. J. Kunnen and C. Siewert and M. Meinke and W. Schröder and K.D. Beheng}, editor = {Elsevier}, url = {http://www.sciencedirect.com/science/article/pii/S0169809513000549 10.1016/j.atmosres.2013.02.003}, year = {2013}, date = {2013-05-15}, journal = {Atmospheric Research}, abstract = {The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point-particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 μm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm2 s− 3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to gravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature.}, } The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point-particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 μm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm2 s− 3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to gravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature. |

R. P. J. Kunnen C. Siewert, Meinke Schröder Beheng Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds (Artikel) Atmospheric Research, 127, Seite(n): 8–21, 2013, ISSN: 0169-8095. @article{Kunnen2013, name = {Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds}, author = {R. P. J. Kunnen, C. Siewert, M. Meinke, W. Schröder, K.D. Beheng}, url = {http://www.sciencedirect.com/science/article/pii/S0169809513000549}, issn = {0169-8095}, year = {2013}, date = {2013-06-01}, journal = {Atmospheric Research}, volume = {127}, pages = {8–21}, abstract = {The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 μm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm2 s− 3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to gravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature.}, } The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 μm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm2 s− 3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to gravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature. |

G. J. Gassner, Beck On the accuracy of high-order discretizations for underresolved turbulence simulations (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 221-237, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Gassner2013, name = {On the accuracy of high-order discretizations for underresolved turbulence simulations}, author = { G. J. Gassner, A. D. Beck }, url = {http://link.springer.com/article/10.1007/s00162-011-0253-7}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {221-237}, abstract = {In this paper, we investigate the accuracy of a high-order discontinuous Galerkin discretization for the coarse resolution simulation of turbulent flow. We show that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing. Thus, for high-order simulations of underresolved turbulence, proper stabilization is necessary for a successful computation. Two different mechanisms are chosen, and their impact on the accuracy of underresolved high-order computations of turbulent flows is investigated. Results of these approximations for the Taylor–Green Vortex problem are compared to direct numerical simulation results from literature. Our findings show that the superior discretization properties of high-order approximations are retained even for these coarsely resolved computations.}, } In this paper, we investigate the accuracy of a high-order discontinuous Galerkin discretization for the coarse resolution simulation of turbulent flow. We show that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing. Thus, for high-order simulations of underresolved turbulence, proper stabilization is necessary for a successful computation. Two different mechanisms are chosen, and their impact on the accuracy of underresolved high-order computations of turbulent flows is investigated. Results of these approximations for the Taylor–Green Vortex problem are compared to direct numerical simulation results from literature. Our findings show that the superior discretization properties of high-order approximations are retained even for these coarsely resolved computations. |

C. Siewert R. P. J. Kunnen, Meinke; Schröder, Orientation Statistics and Settling Velocity of Ellipsoids in Decaying Turbulence (Artikel) Atmospheric Research, 2013. @article{Siewert2013, name = {Orientation Statistics and Settling Velocity of Ellipsoids in Decaying Turbulence}, author = {C. Siewert, R. P. J. Kunnen, M. Meinke and W. Schröder}, note = {In Press}, year = {2013}, date = {2013-10-01}, journal = {Atmospheric Research}, abstract = {Motivated by applications in technology as well as in other disciplines where the motion of particles in a turbulent flow field is important, the orientation and settling velocity of ellipsoidal particles in a spatially decaying isotropic turbulent flow are numerically investigated. With respect to cloud microphysics ellipsoidal particles of various shapes are interpreted as archetypes of regular ice crystals, i.e., plates and columns approximated by oblate and prolate ellipsoids. The motion of 19 million small and heavy ellipsoidal particles is tracked by a Lagrangian point-particle model based on Stokes flow conditions. Five types of ellipsoids of revolution such as prolates, spheres, and oblates are considered. The orientation and settling velocity statistics are gathered at six turbulence intensities characterized by the turbulent kinetic energy dissipation rate ranging from 30 to 250 cm2s− 3. It is shown that the preferential orientation of ellipsoids is disturbed by the turbulent fluctuations of the fluid forces and moments. As the turbulence intensity increases the orientation probability distribution becomes more and more uniform. That is, the settling velocity of the ellipsoids is influenced by the turbulence level since the drag force is dependent on the orientation. The effect is more pronounced, the longer the prolate or the flatter the oblate is. The theoretical settling velocity based on the orientation probability of the non-spherical particles is smaller than that found in the simulation. The results show the existence of the preferential sweeping phenomenon also for non-spherical particles. These two effects of turbulence on the motion of ellipsoids change the settling velocity and as such the swept volume, that is expected to result in modified collision probabilities of ellipsoid-shaped particles.}, note = {In Press}, } Motivated by applications in technology as well as in other disciplines where the motion of particles in a turbulent flow field is important, the orientation and settling velocity of ellipsoidal particles in a spatially decaying isotropic turbulent flow are numerically investigated. With respect to cloud microphysics ellipsoidal particles of various shapes are interpreted as archetypes of regular ice crystals, i.e., plates and columns approximated by oblate and prolate ellipsoids. The motion of 19 million small and heavy ellipsoidal particles is tracked by a Lagrangian point-particle model based on Stokes flow conditions. Five types of ellipsoids of revolution such as prolates, spheres, and oblates are considered. The orientation and settling velocity statistics are gathered at six turbulence intensities characterized by the turbulent kinetic energy dissipation rate ranging from 30 to 250 cm2s− 3. It is shown that the preferential orientation of ellipsoids is disturbed by the turbulent fluctuations of the fluid forces and moments. As the turbulence intensity increases the orientation probability distribution becomes more and more uniform. That is, the settling velocity of the ellipsoids is influenced by the turbulence level since the drag force is dependent on the orientation. The effect is more pronounced, the longer the prolate or the flatter the oblate is. The theoretical settling velocity based on the orientation probability of the non-spherical particles is smaller than that found in the simulation. The results show the existence of the preferential sweeping phenomenon also for non-spherical particles. These two effects of turbulence on the motion of ellipsoids change the settling velocity and as such the swept volume, that is expected to result in modified collision probabilities of ellipsoid-shaped particles. |

Klein, Preface: multiple scales in fluid dynamics and meteorology (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 219-220, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Klein2013, name = {Preface: multiple scales in fluid dynamics and meteorology}, author = {R. Klein}, url = {http://link.springer.com/article/10.1007/s00162-013-0298-x}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {219-220}, } |

Y. Frenkel A. J. Majda, Khouider Simple models for the diurnal cycle and convectively coupled waves (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 533-559, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Frenkel2013, name = {Simple models for the diurnal cycle and convectively coupled waves}, author = {Y. Frenkel, A. J. Majda, B. Khouider }, url = {http://link.springer.com/article/10.1007/s00162-012-0291-9}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {533-559}, abstract = {This paper presents a study of the diurnal cycle of tropical precipitation and its interaction with convectively coupled waves in the context of simple models with crude vertical resolution. One and two baroclinic mode models are tested in both the context of a one-column model and the context of a full spatial dependency that permits waves to propagate and interact with the diurnal cycle. It is found that a one baroclinic mode model is capable of reproducing a realistic diurnal cycle of tropical precipitation both over land and over the ocean provided an adequate switch function is used to mimic the congestus preconditioning mechanism that operates in the multicloud model of Khouider and Majda. However, a full two baroclinic mode multicloud model is needed to capture the interaction of convectively coupled tropical waves with the diurnal cycle. In a more conventional mass flux parameterization framework, both one and two baroclinic mode models fail to capture the diurnal cycle of tropical precipitation.}, } This paper presents a study of the diurnal cycle of tropical precipitation and its interaction with convectively coupled waves in the context of simple models with crude vertical resolution. One and two baroclinic mode models are tested in both the context of a one-column model and the context of a full spatial dependency that permits waves to propagate and interact with the diurnal cycle. It is found that a one baroclinic mode model is capable of reproducing a realistic diurnal cycle of tropical precipitation both over land and over the ocean provided an adequate switch function is used to mimic the congestus preconditioning mechanism that operates in the multicloud model of Khouider and Majda. However, a full two baroclinic mode multicloud model is needed to capture the interaction of convectively coupled tropical waves with the diurnal cycle. In a more conventional mass flux parameterization framework, both one and two baroclinic mode models fail to capture the diurnal cycle of tropical precipitation. |

B. Khouider, Han Simulation of convectively coupled waves using WRF: a framework for assessing the effects of mesoscales on synoptic scales (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 473-489, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Khouider2013, name = {Simulation of convectively coupled waves using WRF: a framework for assessing the effects of mesoscales on synoptic scales}, author = {B. Khouider, Y. Han }, url = {http://link.springer.com/article/10.1007/s00162-012-0276-8}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {473-489}, abstract = {The atmospheric variability in the tropics is primarily driven by convective heating. Observations revealed that convection in the tropics is organized into a hierarchy of multiscale convective systems ranging from the individual cloud cells to planetary scale disturbances that are nested within each other like Russian dolls. Current global climate models simulate very poorly these convectively coupled waves due in part to inadequate treatment of organized convection by the underlying cumulus parameterizations. Here, we present idealized simulations of convectively coupled equatorial waves (CCWs) using the weather research and forecast model in a horizontally limited domain consisting of a 4,500 km-wide square centered at the equator at moderate horizontal resolution of 10 km. We attempted and compared various configuration options, including switching on and off the cumulus parameterization (CP) and nesting a fine resolution 3.33 km domain, a 2,000 km-wide square, in the middle of the domain. It turns out that the results without a CP are much superior than those using a CP. While the cases without a CP resulted in a coherent eastward propagating CCW, which has many common features with observed convectively coupled Kelvin waves, the cumulus parameterization tends to destroy both the coherence of the propagating waves, even in the case with a nested domain, and reduces dramatically the variability. A primary demonstration on how such results could be used to show evidence of energy exchange, through momentum transport, between small-scale circulation due to mesoscale convection and the propagating synoptic scale wave will be reported is also presented.}, } The atmospheric variability in the tropics is primarily driven by convective heating. Observations revealed that convection in the tropics is organized into a hierarchy of multiscale convective systems ranging from the individual cloud cells to planetary scale disturbances that are nested within each other like Russian dolls. Current global climate models simulate very poorly these convectively coupled waves due in part to inadequate treatment of organized convection by the underlying cumulus parameterizations. Here, we present idealized simulations of convectively coupled equatorial waves (CCWs) using the weather research and forecast model in a horizontally limited domain consisting of a 4,500 km-wide square centered at the equator at moderate horizontal resolution of 10 km. We attempted and compared various configuration options, including switching on and off the cumulus parameterization (CP) and nesting a fine resolution 3.33 km domain, a 2,000 km-wide square, in the middle of the domain. It turns out that the results without a CP are much superior than those using a CP. While the cases without a CP resulted in a coherent eastward propagating CCW, which has many common features with observed convectively coupled Kelvin waves, the cumulus parameterization tends to destroy both the coherence of the propagating waves, even in the case with a nested domain, and reduces dramatically the variability. A primary demonstration on how such results could be used to show evidence of energy exchange, through momentum transport, between small-scale circulation due to mesoscale convection and the propagating synoptic scale wave will be reported is also presented. |

Scheck L., Jones; Heuveline, Singular Vectors for barotropic, hurricane-like vortices in horizontal shear: Structure and perturbation growth mechanisms (Artikel) Journal of the Atmospheric Sciences, 2013, ISSN: Online: 1520-0469 Print: 0022-4928 . @article{Scheck2013, name = {Singular Vectors for barotropic, hurricane-like vortices in horizontal shear: Structure and perturbation growth mechanisms}, author = {Scheck, L., Jones, S.C. and Heuveline, V.}, note = {accepted 10.1175/JAS-D-13-0226.1}, url = { http://dx.doi.org/10.1175/JAS-D-13-0226.1}, issn = {Online: 1520-0469 Print: 0022-4928 }, year = {2013}, date = {2013-11-01}, journal = {Journal of the Atmospheric Sciences}, abstract = {In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f- and β-planes using a non-divergent barotropic model. With increasing shear strength the singular values for stable vortices increase and the sensitive regions extend further away from the vortex. The formation of β gyres leads to significant changes in the SV structure, but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the inital SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes a additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear the SVs for unstable vortices grow by the same mechanism as for stable vortices.}, note = {accepted 10.1175/JAS-D-13-0226.1}, } In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f- and β-planes using a non-divergent barotropic model. With increasing shear strength the singular values for stable vortices increase and the sensitive regions extend further away from the vortex. The formation of β gyres leads to significant changes in the SV structure, but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the inital SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes a additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear the SVs for unstable vortices grow by the same mechanism as for stable vortices. |

S. Remmler, Hickel Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 319-336, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Remmler2013, name = {Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation}, author = {S. Remmler, S. Hickel }, url = {http://link.springer.com/article/10.1007/s00162-012-0259-9}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {319-336}, abstract = {Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.}, } Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean. |

S. I. Dolaptchiev U. Achatz, Timofeyev Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 297-317, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Dolaptchiev2013, name = {Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation}, author = {S. I. Dolaptchiev, U. Achatz, I. Timofeyev }, url = {http://link.springer.com/article/10.1007/s00162-012-0270-1}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {297-317}, abstract = {We present a new approach for the construction of stochastic subgrid scale parameterizations. Starting from a high-resolution finite-difference discretization of some model equations, the new approach is based on splitting the model variables into fast, small-scale and slow, large-scale modes by averaging the model discretization over neighboring grid cells. After that, the fast modes are eliminated by applying a stochastic mode reduction procedure. This procedure is a generalization of the mode reduction strategy proposed by Majda, Timofeyev & Vanden-Eijnden, in that it allows for oscillations in the closure assumption. The new parameterization is applied to the forced Burgers equation and is compared with a Smagorinsky-type subgrid scale closure.}, } We present a new approach for the construction of stochastic subgrid scale parameterizations. Starting from a high-resolution finite-difference discretization of some model equations, the new approach is based on splitting the model variables into fast, small-scale and slow, large-scale modes by averaging the model discretization over neighboring grid cells. After that, the fast modes are eliminated by applying a stochastic mode reduction procedure. This procedure is a generalization of the mode reduction strategy proposed by Majda, Timofeyev & Vanden-Eijnden, in that it allows for oscillations in the closure assumption. The new parameterization is applied to the forced Burgers equation and is compared with a Smagorinsky-type subgrid scale closure. |

E. Dietze J. P. Mellado, Stevens Schmidt Study of low-order numerical effects in the two-dimensional cloud-top mixing layer (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 239-251, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Dietze2013, name = {Study of low-order numerical effects in the two-dimensional cloud-top mixing layer}, author = {E. Dietze, J. P. Mellado, B. Stevens, H. Schmidt }, url = {http://link.springer.com/article/10.1007/s00162-012-0263-0}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {239-251}, abstract = {Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES.}, } Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES. |

T. v. Larcher A. Fournier, Hollerbach The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 433-451, 2013, ISBN: 0935-4964 (Print) 1432-2250 (Online). @article{Larcher2013, name = {The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface}, author = {T. v. Larcher, A. Fournier, R. Hollerbach }, url = {http://link.springer.com/article/10.1007/s00162-012-0289-3}, isbn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {433-451}, abstract = {We present results of a linear stability analysis of non-axisymmetric thermally driven flows in the classical model of the rotating cylindrical gap of fluid with a horizontal temperature gradient [inner (outer) sidewall cool (warm)] and a sloping bottom endwall configuration where fluid depth increases with radius. For comparison, results of a flat-bottomed endwall case study are also discussed. In both cases, the model setup has a free top surface. The analysis is carried out numerically using a Fourier–Legendre spectral element method (in azimuth and in the meridional plane, respectively) well suited to handle the axisymmetry of the fluid container. We find significant differences between the neutral stability curve for the sloping and the flat-bottomed endwall configuration. In case of a sloping bottom endwall, the wave flow regime is extended to lower rotation rates, that is, the transition curve is shifted systematically to lower Taylor numbers. Moreover, in the sloping bottom endwall case, a sharp reversal of the instability curve is found in its upper part, that is, at large temperature differences, whereas the instability line becomes almost horizontal in the flat-bottomed endwall case. The linear onset of instability is then almost independent of the rotation rate.}, } We present results of a linear stability analysis of non-axisymmetric thermally driven flows in the classical model of the rotating cylindrical gap of fluid with a horizontal temperature gradient [inner (outer) sidewall cool (warm)] and a sloping bottom endwall configuration where fluid depth increases with radius. For comparison, results of a flat-bottomed endwall case study are also discussed. In both cases, the model setup has a free top surface. The analysis is carried out numerically using a Fourier–Legendre spectral element method (in azimuth and in the meridional plane, respectively) well suited to handle the axisymmetry of the fluid container. We find significant differences between the neutral stability curve for the sloping and the flat-bottomed endwall configuration. In case of a sloping bottom endwall, the wave flow regime is extended to lower rotation rates, that is, the transition curve is shifted systematically to lower Taylor numbers. Moreover, in the sloping bottom endwall case, a sharp reversal of the instability curve is found in its upper part, that is, at large temperature differences, whereas the instability line becomes almost horizontal in the flat-bottomed endwall case. The linear onset of instability is then almost independent of the rotation rate. |

J. Schröttle, Dörnbrack Turbulence structure in a diabatically heated forest canopy composed of fractal Pythagoras trees (Artikel) Theoretical and Computational Fluid Dynamics, 27, 3-4, Seite(n): 337-359, 2013, ISSN: 0935-4964 (Print) 1432-2250 (Online). @article{Schröttle2013, name = {Turbulence structure in a diabatically heated forest canopy composed of fractal Pythagoras trees}, author = {J. Schröttle, A. Dörnbrack }, url = {http://link.springer.com/article/10.1007/s00162-012-0284-8}, issn = {0935-4964 (Print) 1432-2250 (Online)}, year = {2013}, date = {2013-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {27}, number = {3-4}, pages = {337-359}, abstract = {We investigate the turbulent flow through a heterogeneous forest canopy by high-resolution numerical modeling. For this purpose, a novel approach to model individual trees is implemented in our large-eddy simulation (LES). A group of sixteen fractal Pythagoras trees is placed in the computational domain and the tree elements are numerically treated as immersed boundaries. Our objective is to resolve the multiscale flow response starting at the diameter of individual tree elements up to the depth of the atmospheric surface layer. A reference run, conducted for the forest flow under neutral thermal stratification, produces physically meaningful turbulence statistics. Our numerical results agree quantitatively with data obtained from former field-scale LESs and wind tunnel experiments. Furthermore, the numerical simulations resolve vortex shedding behind individual branches and trunks as well as the integral response of the turbulent flow through the heterogeneous forest canopy. A focus is the investigation of the turbulence structure of the flow under stable thermal stratification and in response to the heating of the fractal tree crowns. For the stratified flows, statistical quantities, e.g. turbulent kinetic energy and vorticity, are presented and the turbulent exchange processes of momentum and heat are considered in detail. The onset and formation of coherent structures such as elevated shear layers above the diabatically heated forest canopy are analyzed. For the stably stratified flow, temperature ramps above the forest canopy were simulated in agreement with previous observations. Thermally driven vortices with a typical diameter of the canopy height were simulated when the tree crowns were diabatically heated. The impact of the coherent flow structures on the heat flux is investigated.}, } We investigate the turbulent flow through a heterogeneous forest canopy by high-resolution numerical modeling. For this purpose, a novel approach to model individual trees is implemented in our large-eddy simulation (LES). A group of sixteen fractal Pythagoras trees is placed in the computational domain and the tree elements are numerically treated as immersed boundaries. Our objective is to resolve the multiscale flow response starting at the diameter of individual tree elements up to the depth of the atmospheric surface layer. A reference run, conducted for the forest flow under neutral thermal stratification, produces physically meaningful turbulence statistics. Our numerical results agree quantitatively with data obtained from former field-scale LESs and wind tunnel experiments. Furthermore, the numerical simulations resolve vortex shedding behind individual branches and trunks as well as the integral response of the turbulent flow through the heterogeneous forest canopy. A focus is the investigation of the turbulence structure of the flow under stable thermal stratification and in response to the heating of the fractal tree crowns. For the stratified flows, statistical quantities, e.g. turbulent kinetic energy and vorticity, are presented and the turbulent exchange processes of momentum and heat are considered in detail. The onset and formation of coherent structures such as elevated shear layers above the diabatically heated forest canopy are analyzed. For the stably stratified flow, temperature ramps above the forest canopy were simulated in agreement with previous observations. Thermally driven vortices with a typical diameter of the canopy height were simulated when the tree crowns were diabatically heated. The impact of the coherent flow structures on the heat flux is investigated. |

Klein R., Benacchio; O'Neill, Using the sound-proof limit for balanced data initialization (Artikel) 2013. @article{Klein2013, name = {Using the sound-proof limit for balanced data initialization}, author = {Klein, R., Benacchio, T. and O'Neill, W.P.}, note = {ECMWF Seminar on Numerical Methods for Atmosphere and Ocean Modelling, 2-5 September 2013}, url = {http://www.ecmwf.int/newsevents/meetings/annual_seminar/2013/presentations/Klein.pdf}, year = {2013}, date = {2013-09-02}, abstract = {There is substantial theoretical evidence that the pseudo-incompressible model (Durran 1989) is a valid approximation to the equations of fully compressible flow in meso-scale atmospheric flow regimes. Arguably, numerical methods for the integration of the compressible flow equations should then produce essentially pseudoincompressible results at low flow speeds if the initial data are acoustically balanced. This paper summarizes the construction of a compressible flow solver that observes this desirable. Given a pseudo-incompressible solver, the design of the scheme requires little additional coding as it exploits the close structural similarity of the compressible and pseudo-incompressible model equations. The modified scheme allows us to solve the compressible, pseudo-incompressible, and a continuous family of intermediate models, all of which conserve a model-dependent total energy. We conjecture that such a continuous transition from the full dynamics to a balanced model can be utilized for balanced data assimilation.}, note = {ECMWF Seminar on Numerical Methods for Atmosphere and Ocean Modelling, 2-5 September 2013}, } There is substantial theoretical evidence that the pseudo-incompressible model (Durran 1989) is a valid approximation to the equations of fully compressible flow in meso-scale atmospheric flow regimes. Arguably, numerical methods for the integration of the compressible flow equations should then produce essentially pseudoincompressible results at low flow speeds if the initial data are acoustically balanced. This paper summarizes the construction of a compressible flow solver that observes this desirable. Given a pseudo-incompressible solver, the design of the scheme requires little additional coding as it exploits the close structural similarity of the compressible and pseudo-incompressible model equations. The modified scheme allows us to solve the compressible, pseudo-incompressible, and a continuous family of intermediate models, all of which conserve a model-dependent total energy. We conjecture that such a continuous transition from the full dynamics to a balanced model can be utilized for balanced data assimilation. |

## 2012 |

Mukhopadhyay,; Carneiro,; Jasor,; Polifke, A Comparative Assessment of Presumed Function Method of Moments and Quadrature Method of Moments for Simulation of Polydisperse Flows (Konferenz) XXIII ICTAM - - International Congress on Theoretical and Applied Mechanics, 2012. @conference{Mukhopadhyay2012.1, name = {A Comparative Assessment of Presumed Function Method of Moments and Quadrature Method of Moments for Simulation of Polydisperse Flows}, author = {Mukhopadhyay, A. and Carneiro, J. and Jasor, G. and Polifke, W.}, editor = {XXIII ICTAM - - International Congress on Theoretical and Applied Mechanics}, url = {Theoretical and Applied Mechanics, Event Location: Beijing, China, August 19--24 }, year = {2012}, date = {2012-08-19}, booktitle = {XXIII ICTAM - - International Congress on Theoretical and Applied Mechanics}, } |

Park S.B., Baik Raasch; Letzel, A large-eddy simulation study of thermal effects on turbulent flow and dispersion in and above a street canyon (Artikel) J. Appl. Meteor. Climatol., 51, 5, Seite(n): 829-841, 2012, ISSN: Online: 1558-8432 Print: 1558-8424 . @article{Park2012, name = {A large-eddy simulation study of thermal effects on turbulent flow and dispersion in and above a street canyon}, author = {Park, S.B., Baik,J.J., Raasch, S. and Letzel, M.O.}, url = {http://journals.ametsoc.org/doi/abs/10.1175/JAMC-D-11-0180.1}, issn = {Online: 1558-8432 Print: 1558-8424 }, year = {2012}, date = {2012-02-23}, journal = {J. Appl. Meteor. Climatol.}, volume = {51}, number = {5}, pages = {829-841}, abstract = {Thermal effects on turbulent flow and dispersion in and above an idealized street canyon with a street aspect ratio of 1 are numerically investigated using the parallelized large-eddy simulation model (“PALM”). Each of upwind building wall, street bottom, and downwind building wall is heated, and passive scalars are emitted from the street bottom. When compared with the neutral (no heating) case, the heating of the upwind building wall or street bottom strengthens a primary vortex in the street canyon and the heating of the downwind building wall induces a shrunken primary vortex and a winding flow between the vortex and the downwind building wall. Heating also induces higher turbulent kinetic energy and stronger turbulent fluxes at the rooftop height. In the neutral case, turbulent eddies generated by shear instability dominate mixing at the rooftop height and appear as band-shaped perturbations in the time–space plots of turbulent momentum and scalar fluxes. In all of the heating cases, buoyancy-generated turbulent eddies as well as shear-generated turbulent eddies contribute to turbulent momentum and scalar fluxes and band-shaped or lump-shaped perturbations appear at the rooftop height. A quadrant analysis shows that at the rooftop height, in the neutral case and in the case with upwind building-wall heating, sweep events are less frequent but contribute more to turbulent momentum flux than do ejection events. By contrast, in the case with street-bottom and downwind building-wall heating, the frequency of sweep events is similar to that of ejection events and the contribution of ejection events to turbulent momentum flux is comparable to that of sweep events.}, } Thermal effects on turbulent flow and dispersion in and above an idealized street canyon with a street aspect ratio of 1 are numerically investigated using the parallelized large-eddy simulation model (“PALM”). Each of upwind building wall, street bottom, and downwind building wall is heated, and passive scalars are emitted from the street bottom. When compared with the neutral (no heating) case, the heating of the upwind building wall or street bottom strengthens a primary vortex in the street canyon and the heating of the downwind building wall induces a shrunken primary vortex and a winding flow between the vortex and the downwind building wall. Heating also induces higher turbulent kinetic energy and stronger turbulent fluxes at the rooftop height. In the neutral case, turbulent eddies generated by shear instability dominate mixing at the rooftop height and appear as band-shaped perturbations in the time–space plots of turbulent momentum and scalar fluxes. In all of the heating cases, buoyancy-generated turbulent eddies as well as shear-generated turbulent eddies contribute to turbulent momentum and scalar fluxes and band-shaped or lump-shaped perturbations appear at the rooftop height. A quadrant analysis shows that at the rooftop height, in the neutral case and in the case with upwind building-wall heating, sweep events are less frequent but contribute more to turbulent momentum flux than do ejection events. By contrast, in the case with street-bottom and downwind building-wall heating, the frequency of sweep events is similar to that of ejection events and the contribution of ejection events to turbulent momentum flux is comparable to that of sweep events. |

Riechelmann T., Noh; Raasch, A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision (Artikel) New Journal of Physics, 14, 065008, 2012. @article{Riechelmann2012, name = {A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision}, author = {Riechelmann, T., Noh, Y . and Raasch, S. }, url = {http://iopscience.iop.org/1367-2630/14/6/065008/article}, year = {2012}, date = {2012-02-29}, journal = {New Journal of Physics}, volume = {14}, number = {065008}, abstract = {In this paper, a new Lagrangian cloud model (LCM) is introduced in which the flow field is simulated by large-eddy simulation, and the droplets are treated as Lagrangian particles responding to the simulated flow field. In order to handle the extremely large number of droplets within a cloud, the concept of a super-droplet, which represents a large number of real droplets of the same size, is introduced, and the number of contributing real droplets is called the weighting factor. A novel method is developed to realize the collision/coalescence of droplets, in which the consequent variation of the droplet spectrum is represented in terms of the modification of the radius and weighting factor of super-droplets, while keeping the number of super-droplets unchanged. Using an idealized single cloud and trade wind cumuli, the LCM is shown to reproduce the general features of shallow cumulus clouds in agreement with traditional bulk models. The droplet spectrum simulated by the LCM, using collision kernels with and without the effects of turbulence, also shows a pattern consistent with the spectral bin model. Furthermore, the sensitivity of the LCM to two model parameters, the time step and the number of super-droplets, is examined.}, } In this paper, a new Lagrangian cloud model (LCM) is introduced in which the flow field is simulated by large-eddy simulation, and the droplets are treated as Lagrangian particles responding to the simulated flow field. In order to handle the extremely large number of droplets within a cloud, the concept of a super-droplet, which represents a large number of real droplets of the same size, is introduced, and the number of contributing real droplets is called the weighting factor. A novel method is developed to realize the collision/coalescence of droplets, in which the consequent variation of the droplet spectrum is represented in terms of the modification of the radius and weighting factor of super-droplets, while keeping the number of super-droplets unchanged. Using an idealized single cloud and trade wind cumuli, the LCM is shown to reproduce the general features of shallow cumulus clouds in agreement with traditional bulk models. The droplet spectrum simulated by the LCM, using collision kernels with and without the effects of turbulence, also shows a pattern consistent with the spectral bin model. Furthermore, the sensitivity of the LCM to two model parameters, the time step and the number of super-droplets, is examined. |

Metzner Ph., Putzig Horenko Analysis of persistent nonstationary time series and applications (Artikel) Communications in Applied Mathematics and Computational Science, 7, 2, Seite(n): 175–229, 2012. @article{Metzner2014, name = {Analysis of persistent nonstationary time series and applications}, author = {Metzner, Ph., Putzig, L., Horenko, I.}, note = {10.2140/camcos.2012.7.175}, year = {2012}, date = {2012-10-16}, journal = {Communications in Applied Mathematics and Computational Science}, volume = {7}, number = {2}, pages = {175–229}, abstract = {We give an alternative and unified derivation of the general framework developed in the last few years for analyzing nonstationary time series. A different approach for handling the resulting variational problem numerically is introduced. We further expand the framework by employing adaptive finite element algorithms and ideas from information theory to solve the problem of finding the most adequate model based on a maximum-entropy ansatz, thereby reducing the number of underlying probabilistic assumptions. In addition, we formulate and prove the result establishing the link between the optimal parametrizations of the direct and the inverse problems and compare the introduced algorithm to standard approaches like Gaussian mixture models, hidden Markov models, artificial neural networks and local kernel methods. Furthermore, based on the introduced general framework, we show how to create new data analysis methods for specific practical applications. We demonstrate the application of the framework to data samples from toy models as well as to real-world problems such as biomolecular dynamics, DNA sequence analysis and financial applications. }, note = {10.2140/camcos.2012.7.175}, } We give an alternative and unified derivation of the general framework developed in the last few years for analyzing nonstationary time series. A different approach for handling the resulting variational problem numerically is introduced. We further expand the framework by employing adaptive finite element algorithms and ideas from information theory to solve the problem of finding the most adequate model based on a maximum-entropy ansatz, thereby reducing the number of underlying probabilistic assumptions. In addition, we formulate and prove the result establishing the link between the optimal parametrizations of the direct and the inverse problems and compare the introduced algorithm to standard approaches like Gaussian mixture models, hidden Markov models, artificial neural networks and local kernel methods. Furthermore, based on the introduced general framework, we show how to create new data analysis methods for specific practical applications. We demonstrate the application of the framework to data samples from toy models as well as to real-world problems such as biomolecular dynamics, DNA sequence analysis and financial applications. |

Kumar,; Schumacher,; Shaw, Cloud microphysical effects of turbulent mixing and entrainment (Artikel) Theoretical and Computational Fluid Dynamics, 162, 2012, ISSN: Print: 0935-4964; ; Online: 1432-2250. @article{Kumar2012.1, name = {Cloud microphysical effects of turbulent mixing and entrainment}, author = {Kumar, B. and Schumacher, J. and Shaw, R.A.}, editor = {Springer}, url = {http://link.springer.com/article/10.1007%2Fs00162-012-0272-z Doi:10.1007/s00162-012-0272-z }, issn = {Print: 0935-4964; ; Online: 1432-2250}, year = {2012}, date = {2012-06-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {162}, abstract = {Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered. }, } Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered. |

Brdar S., Baldauf Dedner Klöfkorn Comparison of dynamical cores for NWP models (Artikel) Theoretical and Computational Fluid Dynamics, 162, 2012, ISSN: Print: 0935-4964 Online:1432-2250. @article{Brdar2012, name = {Comparison of dynamical cores for NWP models}, author = {Brdar, S., Baldauf, M., Dedner, A., Klöfkorn, R}, editor = {Springer-Verlag}, url = {http://link.springer.com/article/10.1007%2Fs00162-012-0264-z DOI: 10.1007/s00162-012-0264-z}, issn = {Print: 0935-4964 Online:1432-2250}, year = {2012}, date = {2012-04-01}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {162}, abstract = { We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000). }, } We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000). |

Remmler S., Hickel Direct and large-eddy simulation of stratified turbulence (Artikel) International Journal of Heat and Fluid Flow, 35, Seite(n): 13–24, 2012. @article{Remmler 2012, name = {Direct and large-eddy simulation of stratified turbulence}, author = {Remmler, S., Hickel, S.}, url = {http://www.sciencedirect.com/science/article/pii/S0142727X12000458 10.1016/j.ijheatfluidflow.2012.03.009}, year = {2012}, date = {2012-06-05}, journal = {International Journal of Heat and Fluid Flow}, volume = {35}, pages = {13–24}, abstract = {Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.}, } Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid. |

Bipin Kumar Florian Janetzko, Jörg Schumacher; Shaw, Raymond Extreme responses of a coupled scalar–particle system during turbulent mixing (Artikel) New Journal of Physics, 14, Seite(n): 21, 2012, ISSN: 1367-2630. @article{Kumar2012, name = {Extreme responses of a coupled scalar–particle system during turbulent mixing}, author = {Bipin Kumar, Florian Janetzko, Jörg Schumacher and Raymond A Shaw}, url = {http://www.njp.org/ doi:10.1088/1367-2630/14/11/115020}, issn = {1367-2630}, year = {2012}, date = {2012-11-26}, journal = {New Journal of Physics}, volume = {14}, pages = {21}, abstract = {Extreme responses of a droplet ensemble during an entrainment and mixing process as present at the edge of a cloud are investigated by means of three-dimensional direct numerical simulations in the Euler–Lagrangian framework. We find that the Damk¨ohler number Da, a dimensionless parameter which relates the fluid time scale to the typical evaporation time scale, can capture all aspects of the initial mixing process within the range of parameters accessible in this study. The mixing process is characterized by the limits of strongly homogeneous (Da 1) and strongly inhomogeneous (Da 1)regimes. We explore these two extreme regimes and study the response of the droplet size distribution to the corresponding parameter settings through an enhancement and reduction of the response constant K in the droplet growth equation. Thus, Da is varied while Reynolds and Schmidt numbers are held fixed, and initial microphysical properties are held constant. In the homogeneous limit minimal broadening of the size distribution is observed as the new steady state is reached, whereas in the inhomogeneous limit the size distribution develops strong negative skewness, with the appearance of a pronounced exponential tail. The analysis in the Lagrangian framework allows us to relate the pronounced negative tail of the supersaturation distribution to that of the size distribution.}, } Extreme responses of a droplet ensemble during an entrainment and mixing process as present at the edge of a cloud are investigated by means of three-dimensional direct numerical simulations in the Euler–Lagrangian framework. We find that the Damk¨ohler number Da, a dimensionless parameter which relates the fluid time scale to the typical evaporation time scale, can capture all aspects of the initial mixing process within the range of parameters accessible in this study. The mixing process is characterized by the limits of strongly homogeneous (Da 1) and strongly inhomogeneous (Da 1)regimes. We explore these two extreme regimes and study the response of the droplet size distribution to the corresponding parameter settings through an enhancement and reduction of the response constant K in the droplet growth equation. Thus, Da is varied while Reynolds and Schmidt numbers are held fixed, and initial microphysical properties are held constant. In the homogeneous limit minimal broadening of the size distribution is observed as the new steady state is reached, whereas in the inhomogeneous limit the size distribution develops strong negative skewness, with the appearance of a pronounced exponential tail. The analysis in the Lagrangian framework allows us to relate the pronounced negative tail of the supersaturation distribution to that of the size distribution. |

F. Schlegel J. Stiller, Bienert Maas Queck; Bernhofer, Large-Eddy Simulation of inhomogeneous canopy flows using high resolution terrestrial laser scanning data (Artikel) Boundary-Layer Meteorology, 142, Seite(n): 223-243, 2012. @article{1, name = {Large-Eddy Simulation of inhomogeneous canopy flows using high resolution terrestrial laser scanning data}, author = {F. Schlegel, J. Stiller, A. Bienert, H.-G. Maas, R. Queck, and C. Bernhofer}, note = {0006-8314 (Print), 1573-1472 (Online)}, year = {2012}, date = {2012-01-16}, journal = {Boundary-Layer Meteorology}, volume = {142}, pages = {223-243}, abstract = {The effect of sub-tree forest heterogeneity in the flow past a clearing is investigated by means of large-eddy simulation (LES). For this purpose, a detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 190 m length in the field site “Tharandter Wald”, near the city of Dresden, Germany. The scanning data are used to produce a high resolution plant area distribution (PAD) that is averaged over approximately one tree height (30 m) along the transverse direction, in order to simplify the LES study. Despite the smoothing involved with this procedure, the resulting two-dimensional PAD maintains a rich vertical and horizontal structure. For the LES study, the PAD is embedded in a larger domain covered with an idealized, horizontally homogeneous canopy. Simulations are performed for neutral conditions and compared to a LES with homogeneous PAD and recent field measurements. The results reveal a considerable influence of small-scale plant distribution on the mean velocity field as well as on turbulence data. Particularly near the edges of the clearing, where canopy structure is highly variable, usage of a realistic PAD appears to be crucial for capturing the local flow structure. Inside the forest, local variations in plant density induce a complex pattern of upward and downward motions, which remain visible in the mean flow and make it difficult to identify the “adjustment zone” behind the windward edge of the clearing.}, note = {0006-8314 (Print), 1573-1472 (Online)}, } The effect of sub-tree forest heterogeneity in the flow past a clearing is investigated by means of large-eddy simulation (LES). For this purpose, a detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 190 m length in the field site “Tharandter Wald”, near the city of Dresden, Germany. The scanning data are used to produce a high resolution plant area distribution (PAD) that is averaged over approximately one tree height (30 m) along the transverse direction, in order to simplify the LES study. Despite the smoothing involved with this procedure, the resulting two-dimensional PAD maintains a rich vertical and horizontal structure. For the LES study, the PAD is embedded in a larger domain covered with an idealized, horizontally homogeneous canopy. Simulations are performed for neutral conditions and compared to a LES with homogeneous PAD and recent field measurements. The results reveal a considerable influence of small-scale plant distribution on the mean velocity field as well as on turbulence data. Particularly near the edges of the clearing, where canopy structure is highly variable, usage of a realistic PAD appears to be crucial for capturing the local flow structure. Inside the forest, local variations in plant density induce a complex pattern of upward and downward motions, which remain visible in the mean flow and make it difficult to identify the “adjustment zone” behind the windward edge of the clearing. |

Letzel M.O., Helmke Ng; An X., Lai; Raasch, LES case study on pedestrian level ventilation in two neighbourhoods in Hong Kong (Artikel) Meteorologische Zeitschrift, 21, 6, Seite(n): 575-589, 2012. @article{Letzel2012, name = {LES case study on pedestrian level ventilation in two neighbourhoods in Hong Kong}, author = {Letzel, M.O., Helmke, C., Ng, E. and An, X., Lai, A. and Raasch, S.}, url = {http://www.schweizerbart.de/papers/metz/detail/21/79530/LES_case_study_on_pedestrian_level_ventilation_in_}, year = {2012}, date = {2012-02-21}, journal = {Meteorologische Zeitschrift}, volume = {21}, number = {6}, pages = { 575-589}, abstract = {Hong Kong is one of the most densely built-up and populated cities in the world. An adequate air ventilation at pedestrian level would ease the thermal stress in its humid subtropical climate, but the high-density city severely reduces the natural ventilation. This case study investigates pedestrian level ventilation in two neighbourhoods in Kowloon, downtown Hong Kong using the parallelized large-eddy-simulation (LES) model PALM. The LES technique is chosen here for a city quarter scale pedestrian comfort study despite of its high computational cost. The aims of the paper are a) to get a comprehensive overview of pedestrian level ventilation and a better understanding of the ventilation processes in downtown Hong Kong, b) to test the LES technique on this urban scale compared to the wind tunnel and c) to investigate how numerical/physical parameters influence ventilation. This case study is restricted to neutral stratification in order to allow a direct comparison with the wind tunnel. A sensitivity study quantifies the dependence of site-averaged ventilation on numerical and physical parameters and determines an appropriate urban LES set-up for two 1 km2 neighbourhoods in Kowloon (Tsim Sha Tsui, Mong Kok) that are investigated for prevailing E and SW wind. The results reveal the critical dependence of ventilation on the urban morphology. Air paths, street orientations, ground coverage, sites fronting the water, inter connectivity of spaces, building podium size and building heights can all affect the pedestrian wind environment. Isolated tall buildings may have a pronounced impact on ventilation both locally and downstream. }, } Hong Kong is one of the most densely built-up and populated cities in the world. An adequate air ventilation at pedestrian level would ease the thermal stress in its humid subtropical climate, but the high-density city severely reduces the natural ventilation. This case study investigates pedestrian level ventilation in two neighbourhoods in Kowloon, downtown Hong Kong using the parallelized large-eddy-simulation (LES) model PALM. The LES technique is chosen here for a city quarter scale pedestrian comfort study despite of its high computational cost. The aims of the paper are a) to get a comprehensive overview of pedestrian level ventilation and a better understanding of the ventilation processes in downtown Hong Kong, b) to test the LES technique on this urban scale compared to the wind tunnel and c) to investigate how numerical/physical parameters influence ventilation. This case study is restricted to neutral stratification in order to allow a direct comparison with the wind tunnel. A sensitivity study quantifies the dependence of site-averaged ventilation on numerical and physical parameters and determines an appropriate urban LES set-up for two 1 km2 neighbourhoods in Kowloon (Tsim Sha Tsui, Mong Kok) that are investigated for prevailing E and SW wind. The results reveal the critical dependence of ventilation on the urban morphology. Air paths, street orientations, ground coverage, sites fronting the water, inter connectivity of spaces, building podium size and building heights can all affect the pedestrian wind environment. Isolated tall buildings may have a pronounced impact on ventilation both locally and downstream. |

R. Bordás v. John, Schmeyer; Thévénin, Measurement and Simulation of a Droplet Population in a Turbulent Flow Field (Artikel) 2012. @article{1, name = {Measurement and Simulation of a Droplet Population in a Turbulent Flow Field}, author = {R. Bordás, v. John, E. Schmeyer, and D. Thévénin}, editor = {Elsevier}, year = {2012}, date = {2012-01-01}, abstract = {The interaction of a disperse droplet population (spray) in a turbulent flow field is studied by combining wind tunnel experiments with simulations based on the model of a population balance system. The behavior of the droplets is modeled numerically by a population balance equation. Velocities of the air and of the droplets are determined by non-intrusive measurements. A direct discretization of the 4D equation for the droplet size distribution is used in the simulations. Important components of the numerical algorithm are a variational multiscale method for turbulence modeling, an upwind scheme for the 4D equation and a pre-processing approach to evaluate the aggretation integrals. The simulations of this system accurately predict the modifications of the droplet size distribution from the inlet to the outlet of the measurement section. Since the employed configuration is simple and considering that all measurement data are freely available thanks to an Internet-based repository, the considered experiment is proposed as a benchmark problem for the simulation of disperse two-phase turbulent flows.}, } The interaction of a disperse droplet population (spray) in a turbulent flow field is studied by combining wind tunnel experiments with simulations based on the model of a population balance system. The behavior of the droplets is modeled numerically by a population balance equation. Velocities of the air and of the droplets are determined by non-intrusive measurements. A direct discretization of the 4D equation for the droplet size distribution is used in the simulations. Important components of the numerical algorithm are a variational multiscale method for turbulence modeling, an upwind scheme for the 4D equation and a pre-processing approach to evaluate the aggretation integrals. The simulations of this system accurately predict the modifications of the droplet size distribution from the inlet to the outlet of the measurement section. Since the employed configuration is simple and considering that all measurement data are freely available thanks to an Internet-based repository, the considered experiment is proposed as a benchmark problem for the simulation of disperse two-phase turbulent flows. |

John,; Thein, On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM) (Artikel) 2012. @article{1, name = {On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM)}, author = {V. John and F. Thein}, editor = {Chemical Engineering Science, 75:327–333.}, year = {2012}, date = {2012-01-01}, abstract = {Three methods are reviewed for computing optimal weights and abscissas which can be used in the quadrature method of moments (QMOM): the product-difference algorithm (PDA), the long quotient-modified difference algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub–Welsch algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA.}, } Three methods are reviewed for computing optimal weights and abscissas which can be used in the quadrature method of moments (QMOM): the product-difference algorithm (PDA), the long quotient-modified difference algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub–Welsch algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA. |

Ziemer,; Wacker, Parameterisation of the Sedimentation of Raindrops with Finite Maximum Diameter (Artikel) Monthly Weather Review, 140, 5, Seite(n): 1589-1602, 2012, ISSN: 1520-0493 . @article{Ziemer 2012, name = {Parameterisation of the Sedimentation of Raindrops with Finite Maximum Diameter}, author = {Ziemer, C. and Wacker, U.}, editor = {American Meteorological Society}, url = {doi: 10.1175/MWR-D-11-00020.1 }, issn = {1520-0493 }, year = {2012}, date = {2012-05-10}, journal = {Monthly Weather Review}, volume = {140}, number = {5}, pages = {1589-1602}, abstract = {In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model.}, } In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model. |

Ziemer,; Wacker, Parameterisation of the Sedimentation of Raindrops with Finite Maximum Diameter (Artikel) Monthly Weather Review, 140, 5, Seite(n): 1589 -1602, 2012, ISSN: Online: 1520-0493 Print : 0027-0644. @article{Ziemer 2015, name = {Parameterisation of the Sedimentation of Raindrops with Finite Maximum Diameter}, author = {Ziemer, C. and Wacker, U.}, issn = {Online: 1520-0493 Print : 0027-0644}, year = {2012}, date = {2012-05-01}, journal = {Monthly Weather Review}, volume = {140}, number = {5}, pages = {1589 -1602}, abstract = {In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model.}, } In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model. |

Mukhopadhyay A., Jasor Polifke Simulation of Pure Sedimentation of Raindrops using Quadrature Method of Moments (Artikel) J. Atmospheric Research, 106, Seite(n): 61–70, 2012. @article{Mukhopadhyay2012, name = {Simulation of Pure Sedimentation of Raindrops using Quadrature Method of Moments}, author = {Mukhopadhyay, A., Jasor, G., Polifke, W.}, editor = {Elsevier}, url = {http://www.sciencedirect.com/science/article/pii/S0169809511003875}, year = {2012}, date = {2012-03-06}, journal = {J. Atmospheric Research}, volume = {106}, pages = {61–70}, abstract = {The quadrature method of moments (QMOM) is used for simulation of pure sedimentation of raindrops in a one-dimensional rainshaft. The moments have been calculated in three ways, based either on droplet diameter using two and three nodes or on droplet volume using two nodes. The method gives useful information on the range of sizes and also on spatial segregation of the droplets. The results show that all three methods give useful information about the transport processes involved and compare satisfactorily with the spectral (bin) method although use of diameter as internal coordinate is preferable from the viewpoint of quantitative agreement.}, } The quadrature method of moments (QMOM) is used for simulation of pure sedimentation of raindrops in a one-dimensional rainshaft. The moments have been calculated in three ways, based either on droplet diameter using two and three nodes or on droplet volume using two nodes. The method gives useful information on the range of sizes and also on spatial segregation of the droplets. The results show that all three methods give useful information about the transport processes involved and compare satisfactorily with the spectral (bin) method although use of diameter as internal coordinate is preferable from the viewpoint of quantitative agreement. |

M. Braack J. Lang, Taschenberger Stabilized finite elements for transient flow problems on varying spatial meshes (Artikel) Comput. Meth. Appl. Mech. Eng, accepted, 2012. (BibTeX) @article{., name = {Stabilized finite elements for transient flow problems on varying spatial meshes}, author = {M. Braack, J. Lang, N. Taschenberger}, note = {accepted}, year = {2012}, date = {2012-08-23}, journal = {Comput. Meth. Appl. Mech. Eng}, volume = {accepted}, note = {accepted}, } |

## 2011 |

Dedner,; Klöfkorn, A Generic Stabilization Approach for Higher Order Discontinuous Galerkin (Artikel) 2011. @article{1, name = {A Generic Stabilization Approach for Higher Order Discontinuous Galerkin}, author = {A. Dedner and R. Klöfkorn}, editor = {J. Sci. Comput.}, year = {2011}, date = {2011-01-01}, abstract = {submitted}, } submitted |

Jasor,; Wacker,; Beheng,; Polifke, Application of Quadrature Method of Moments for Sedimentation and Coagulation of Raindrops (Konferenz) 2011. @conference{Jasor2011, name = {Application of Quadrature Method of Moments for Sedimentation and Coagulation of Raindrops}, author = {Jasor, G. and Wacker, U. and Beheng, K.D. and Polifke, W.}, editor = {International Metstroem Conference}, year = {2011}, date = {2011-06-06}, organization = {Freie Universität Berlin}, abstract = {The formation and sedimentation of raindrops is described by an integro-differential equation for the size distribution function (”population balance equation”). The numerical solution of this equation by discretization in spatial and property coordinates (spectral, i.e. diameter or mass coordinates) may be straightforward in principle, but is prohibitively expensive in practice. For applications such as numerical weather prediction (NWP), efficient approximations must be formulated. One promising approach is the quadrature method of moments (QMoM), which is quite well-known, e.g., in chemical engineering. With QMoM, a population of particles is described approximately by a few moments of its size distribution, for which transport equations are formulated. Moment transport velocities as well as source terms (due to evaporation/condensation or break-up/coagulation, etc.) are evaluated approximately by Gaussian quadrature. The method is quite flexible and does not make any particular assumptions on the functional form of the size distribution or the break-up/coagulation kernels. In this paper, QMoM is applied to sedimentation of raindrops, taking simultaneously the effects of coagulation into account. Only simple 1D (vertical ”rainshaft”) configurations are considered. This allows the computation of solutions of the population dynamics in a spectral resolution, which serves as a reference solution for validation studies. Results obtained with different coagulation kernel functions show that QMoM properly captures the essential physical behaviour, in general with good quantitative accuracy at very low computational costs.}, } The formation and sedimentation of raindrops is described by an integro-differential equation for the size distribution function (”population balance equation”). The numerical solution of this equation by discretization in spatial and property coordinates (spectral, i.e. diameter or mass coordinates) may be straightforward in principle, but is prohibitively expensive in practice. For applications such as numerical weather prediction (NWP), efficient approximations must be formulated. One promising approach is the quadrature method of moments (QMoM), which is quite well-known, e.g., in chemical engineering. With QMoM, a population of particles is described approximately by a few moments of its size distribution, for which transport equations are formulated. Moment transport velocities as well as source terms (due to evaporation/condensation or break-up/coagulation, etc.) are evaluated approximately by Gaussian quadrature. The method is quite flexible and does not make any particular assumptions on the functional form of the size distribution or the break-up/coagulation kernels. In this paper, QMoM is applied to sedimentation of raindrops, taking simultaneously the effects of coagulation into account. Only simple 1D (vertical ”rainshaft”) configurations are considered. This allows the computation of solutions of the population dynamics in a spectral resolution, which serves as a reference solution for validation studies. Results obtained with different coagulation kernel functions show that QMoM properly captures the essential physical behaviour, in general with good quantitative accuracy at very low computational costs. |

Brdar S., Dedner Klöfkorn Compact and Stable Discontinuous Galerkin Methods with Application to Atmospheric Flows (Artikel) Computational Methods in Science and Engineering : Proceedings of the Workshop SimLabs@KIT, Seite(n): 109-116, 2011, ISBN: 978-3-86644-693-9. @article{Brdar2011, name = {Compact and Stable Discontinuous Galerkin Methods with Application to Atmospheric Flows}, author = {Brdar, S., Dedner, A.,Klöfkorn, R.}, editor = {KIT Scientific Publishing}, url = {http://www.ksp.kit.edu/shop/isbn2shopid.php?isbn=978-3-86644-693-9}, isbn = {978-3-86644-693-9}, year = {2011}, date = {2011-07-11}, journal = {Computational Methods in Science and Engineering : Proceedings of the Workshop SimLabs@KIT}, pages = {109-116}, abstract = {In this work we formulate the Compact Discontinuous Galerkin 2 (CDG2) method introduced in [8] for advection-diffusion problems. We present a proof of stability for the linear heat equation. Numerical results are shown for the compressible Navier-Stokes equation. We compare our new method numerically with two other well-established methods: the Compact Discontinuous Galerkin (CDG) and the Local Discontinuous Galerkin (LDG) method. In contrast to the LDG method, the primal formulation of the CDG2 method only involves the direct neighbors, making it more suitable for execution on parallel computers. The CDG method also has this compactness property, but the performance of the method is not as good as for the CDG2 method in terms of L2-error versus computation time.}, } In this work we formulate the Compact Discontinuous Galerkin 2 (CDG2) method introduced in [8] for advection-diffusion problems. We present a proof of stability for the linear heat equation. Numerical results are shown for the compressible Navier-Stokes equation. We compare our new method numerically with two other well-established methods: the Compact Discontinuous Galerkin (CDG) and the Local Discontinuous Galerkin (LDG) method. In contrast to the LDG method, the primal formulation of the CDG2 method only involves the direct neighbors, making it more suitable for execution on parallel computers. The CDG method also has this compactness property, but the performance of the method is not as good as for the CDG2 method in terms of L2-error versus computation time. |

S. Brinkop C. Kamm, Grewe Jöckel Reich Stenke Sausen Shin; Yserentant, Development of a Lagrangian Dynamical Core for Climate Models (LagKern) (Artikel) 2011. (BibTeX) @article{1, name = {Development of a Lagrangian Dynamical Core for Climate Models (LagKern)}, author = {S. Brinkop, C. Kamm, V. Grewe, P. Jöckel, S. Reich, A. Stenke, R. Sausen, S. Shin, and H. Yserentant}, editor = {Miscellaneous publication.}, year = {2011}, date = {2011-01-01}, } |

R. Bordás T. Hagemeier, Wunderlich; Thévenin, Droplet Collisions and Interaction with the Turbulent Flow within a Two-Phase Wind Tunnel (Artikel) 2011. @article{1, name = {Droplet Collisions and Interaction with the Turbulent Flow within a Two-Phase Wind Tunnel}, author = {R. Bordás, T. Hagemeier, B. Wunderlich, and D. Thévenin}, editor = {Physics of Fluids, 23(8):11 pages.}, year = {2011}, date = {2011-01-01}, abstract = {Experiments in wind tunnels concerning meteorological issues are not very frequent in the literature. However, such experiments might be essential, for instance for a careful investigation of droplet-droplet interactions in turbulent flows. This issue is crucial for many configurations, in particular to understand warm rain initiation. It is clearly impossible to completely reproduce cloud turbulence within a wind tunnel due to the enormous length scales involved. Nevertheless, it is not necessary to recover the whole spectrum in order to quantify droplet interactions. It is sufficient for this purpose to account correctly for the relevant properties only. In the present paper, these properties and a methodology for setting those in a two-phase wind tunnel are first described. In particular, droplet size and number density, velocities, turbulent kinetic energy, k, and its dissipation rate, ɛ, are suitably reproduced, as demonstrated by non-intrusive measurement techniques. A complete experimental characterization of the air and droplet properties is freely available in a database accessible at http://www.ovgu.de/isut/lss/metstroem. Finally, quantifications of droplet collision rates and comparisons with theoretical predictions are presented, showing that measured collision rates are higher, typically by a factor of 2 to 5. These results demonstrate that model modifications are needed to estimate correctly droplet collision probabilities in turbulent flows}, } Experiments in wind tunnels concerning meteorological issues are not very frequent in the literature. However, such experiments might be essential, for instance for a careful investigation of droplet-droplet interactions in turbulent flows. This issue is crucial for many configurations, in particular to understand warm rain initiation. It is clearly impossible to completely reproduce cloud turbulence within a wind tunnel due to the enormous length scales involved. Nevertheless, it is not necessary to recover the whole spectrum in order to quantify droplet interactions. It is sufficient for this purpose to account correctly for the relevant properties only. In the present paper, these properties and a methodology for setting those in a two-phase wind tunnel are first described. In particular, droplet size and number density, velocities, turbulent kinetic energy, k, and its dissipation rate, ɛ, are suitably reproduced, as demonstrated by non-intrusive measurement techniques. A complete experimental characterization of the air and droplet properties is freely available in a database accessible at http://www.ovgu.de/isut/lss/metstroem. Finally, quantifications of droplet collision rates and comparisons with theoretical predictions are presented, showing that measured collision rates are higher, typically by a factor of 2 to 5. These results demonstrate that model modifications are needed to estimate correctly droplet collision probabilities in turbulent flows |

M. Braack E. Burman, Taschenberger Duality based a posteriori error estimation for quasi periodic solutions using time averages (Artikel) SIAM J. Scientific Computing, 33, Seite(n): 2199-2216, 2011, ISSN: 1064-8275. @article{., name = {Duality based a posteriori error estimation for quasi periodic solutions using time averages}, author = {M. Braack, E. Burman, N. Taschenberger}, editor = {Society for Industrial and Applied Mathematics}, issn = {1064-8275}, year = {2011}, date = {2011-09-06}, journal = {SIAM J. Scientific Computing}, volume = {33}, pages = {2199-2216}, abstract = {We propose an a posteriori error estimation technique for the computation of average functionals of solutions for nonlinear time dependent problems based on duality techniques. The exact solution is assumed to have a periodic or quasi-periodic behavior favoring a fixed mesh strategy in time. We show how to circumvent the need of solving time dependent dual problems. The estimator consists of an averaged residual weighted by sensitivity factors coming from a stationary dual problem and an additional averaging error term coming from nonlinearities of the operator considered. In order to illustrate this technique the resulting adaptive algorithm is applied to several model problems: a linear scalar parabolic problem with known exact solution, the nonsteady Navier–Stokes equations with known exact solution, and finally to the well-known benchmark problem for Navier–Stokes (flow behind a cylinder) in order to verify the modeling assumptions.}, } We propose an a posteriori error estimation technique for the computation of average functionals of solutions for nonlinear time dependent problems based on duality techniques. The exact solution is assumed to have a periodic or quasi-periodic behavior favoring a fixed mesh strategy in time. We show how to circumvent the need of solving time dependent dual problems. The estimator consists of an averaged residual weighted by sensitivity factors coming from a stationary dual problem and an additional averaging error term coming from nonlinearities of the operator considered. In order to illustrate this technique the resulting adaptive algorithm is applied to several model problems: a linear scalar parabolic problem with known exact solution, the nonsteady Navier–Stokes equations with known exact solution, and finally to the well-known benchmark problem for Navier–Stokes (flow behind a cylinder) in order to verify the modeling assumptions. |

Denise Hertwig Bernd Leitl,; Schatzmann, Michael Organized turbulent structures –- Link between experimental data and LES (Artikel) 2011. @article{1, name = {Organized turbulent structures –- Link between experimental data and LES}, author = {Denise Hertwig, Bernd Leitl, and Michael Schatzmann}, editor = {Journal of Wind Engineering and Industrial Aerodynamics, 99(4):296-307.}, year = {2011}, date = {2011-01-01}, abstract = {Methods of eddy structure identification are applied to velocity data of atmospheric surface layer flows modeled in a boundary-layer wind tunnel. The objective is to test their potential to serve as mathematical tools for the validation of eddy-resolving numerical models like large-eddy simulation and for the generation of realistic turbulent inflow conditions. The reconstruction of complex atmospheric flows on the basis of two-point space-time statistics is tested with the proper orthogonal decomposition and linear stochastic estimation that are both applied to spatially well-resolved flow data. The continuous wavelet transform is used to derive joint time-frequency information from single-point velocity time series. Whereas the proper orthogonal decomposition and the continuous wavelet transform show particular strengths in the spatiotemporal characterization of turbulent flows, the stochastic estimation is moreover qualified to generate new flow scenarios from a minimum number of instantaneous data.}, } Methods of eddy structure identification are applied to velocity data of atmospheric surface layer flows modeled in a boundary-layer wind tunnel. The objective is to test their potential to serve as mathematical tools for the validation of eddy-resolving numerical models like large-eddy simulation and for the generation of realistic turbulent inflow conditions. The reconstruction of complex atmospheric flows on the basis of two-point space-time statistics is tested with the proper orthogonal decomposition and linear stochastic estimation that are both applied to spatially well-resolved flow data. The continuous wavelet transform is used to derive joint time-frequency information from single-point velocity time series. Whereas the proper orthogonal decomposition and the continuous wavelet transform show particular strengths in the spatiotemporal characterization of turbulent flows, the stochastic estimation is moreover qualified to generate new flow scenarios from a minimum number of instantaneous data. |

S. Jebens O. Knoth, Weiner Partially Implicit PeerMethods for the Compressible Euler Equations (Artikel) 2011. (BibTeX) @article{1, name = {Partially Implicit PeerMethods for the Compressible Euler Equations}, author = {S. Jebens, O. Knoth, R. Weiner}, editor = {Journal of Computational Physics.}, year = {2011}, date = {2011-01-01}, } |

Uwe Harlander Thomas von Larcher, Yongtai Wang; Egbers, Christoph PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus (Artikel) 2011. @article{1, name = {PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus}, author = {Uwe Harlander, Thomas von Larcher, Yongtai Wang, and Christoph Egbers}, editor = {Experiments in Fluids, 51:37-49.}, year = {2011}, date = {2011-01-01}, abstract = {We present results of experiments in a rotating, baroclinic annulus of fluid. The apparatus is a differentially heated cylindrical gap with a flat bottom topography and a free surface, rotated around its vertical axis of symmetry, cooled from within, and filled with de-ionised water as working fluid. We used multivariate statistical techniques to understand better the variability of the heated rotating flow $(a)$ in the transition region between regular waves of different zonal wave number, and $(b)$ in the transition region to the quasi-chaotic regime. The former regime is studied by applying the Complex Empirical Orthogonal Function (CEOF) method to Particle-Image-Velocimetry (PIV) data, the latter by applying the Multi-Channel Singular Spectrum Analysis (M-SSA) to Laser-Doppler-Velocimetry (LDV) data. In the annulus, interactions between the dominant mode and so called weaker modes can lead to low-frequency amplitude and wave structure vacillations. Our results complement previous observations recovered primarily by thermocouple arrangements.}, } We present results of experiments in a rotating, baroclinic annulus of fluid. The apparatus is a differentially heated cylindrical gap with a flat bottom topography and a free surface, rotated around its vertical axis of symmetry, cooled from within, and filled with de-ionised water as working fluid. We used multivariate statistical techniques to understand better the variability of the heated rotating flow $(a)$ in the transition region between regular waves of different zonal wave number, and $(b)$ in the transition region to the quasi-chaotic regime. The former regime is studied by applying the Complex Empirical Orthogonal Function (CEOF) method to Particle-Image-Velocimetry (PIV) data, the latter by applying the Multi-Channel Singular Spectrum Analysis (M-SSA) to Laser-Doppler-Velocimetry (LDV) data. In the annulus, interactions between the dominant mode and so called weaker modes can lead to low-frequency amplitude and wave structure vacillations. Our results complement previous observations recovered primarily by thermocouple arrangements. |

U. Harlander J. Wenzel, Alexandrov Wang; Egbers, Simultaneous PIV- and thermography-measurements of partially blocked flow in a differentially heated rotating annulus (Artikel) 2011. @article{1, name = {Simultaneous PIV- and thermography-measurements of partially blocked flow in a differentially heated rotating annulus}, author = {U. Harlander, J. Wenzel, K. Alexandrov, Y. Wang, and C. Egbers}, editor = {Experiments in Fluids.}, note = {submitted}, year = {2011}, date = {2011-01-01}, abstract = {A radial barrier has been mounted in a diﬀerentially heated rotating annulus that partially blocks the azimuthal ﬂow component. The experiment can be seen as an analogue to geophysical ﬂows with constrictions, e.g. the Antarctic Circumpolar Current. However, the experiment has been carried out without a particular natural ﬂow in mind. The main interest was to observe a baroclinic annulus ﬂow that does not become saturated. Hence, in contrast to the annulus ﬂow without a barrier, the partially blocked ﬂow remains transient and surface heat ﬂuxes associated with baroclinic life cycles can be studied. The annulus can be subdivided into the upstream half of the barrier, where waves amplify, and the downstream half of the barrier, where waves decay. In the upstream half, the azimuthal mean ﬂow is moderate but with a signiﬁcant positive eddy radial heat ﬂux. In the downstream half, we ﬁnd a strong jet in the mean azimuthal ﬂow and furthermore an increased radial mean temperature gradient. The latter points to a weakened or even reversed radial eddy heat ﬂux in the lee side of the barrier. Temperature anomalies appear as large bulges in the outer part of the annulus. Moreover, an outward shift of vortex centers can be observed with respect to centers of temperature anomalies. This phase shift between pressure and temperature anomalies diﬀers from that of classical Eady modes of baroclinic intability.}, note = {submitted}, } A radial barrier has been mounted in a diﬀerentially heated rotating annulus that partially blocks the azimuthal ﬂow component. The experiment can be seen as an analogue to geophysical ﬂows with constrictions, e.g. the Antarctic Circumpolar Current. However, the experiment has been carried out without a particular natural ﬂow in mind. The main interest was to observe a baroclinic annulus ﬂow that does not become saturated. Hence, in contrast to the annulus ﬂow without a barrier, the partially blocked ﬂow remains transient and surface heat ﬂuxes associated with baroclinic life cycles can be studied. The annulus can be subdivided into the upstream half of the barrier, where waves amplify, and the downstream half of the barrier, where waves decay. In the upstream half, the azimuthal mean ﬂow is moderate but with a signiﬁcant positive eddy radial heat ﬂux. In the downstream half, we ﬁnd a strong jet in the mean azimuthal ﬂow and furthermore an increased radial mean temperature gradient. The latter points to a weakened or even reversed radial eddy heat ﬂux in the lee side of the barrier. Temperature anomalies appear as large bulges in the outer part of the annulus. Moreover, an outward shift of vortex centers can be observed with respect to centers of temperature anomalies. This phase shift between pressure and temperature anomalies diﬀers from that of classical Eady modes of baroclinic intability. |

R. Queck A. Bienert, Maas Hermansa Goldberg; Bernhofer, Wind fields in heterogeneous conifer canopies: parameterisation of momentum absorption using high-resolution 3D vegetation scans (Artikel) 2011. @article{1, name = {Wind fields in heterogeneous conifer canopies: parameterisation of momentum absorption using high-resolution 3D vegetation scans}, author = {R. Queck, A. Bienert, H.G. Maas, S. Hermansa, V. Goldberg, and C. Bernhofer}, editor = {European Journal of Forest Research.}, note = {SpringerLink; 1612-4669 (Print) 1612-4677 (Online)}, year = {2011}, date = {2011-01-01}, abstract = {Applications of flow models to tall plant canopies are limited, amongst other factors, by the lack of detailed information on vegetation structure. A method is presented to record 3D vegetation structure and make this information applicable to the derivation of turbulence parameters suitable for flow models. The relationship between wind speed, drag coefficient (CD) and plant area density (PAD) was experimentally investigated in a mixed conifer forest in the lower part of the Eastern Ore Mountains. Essential information was gathered by collecting multi-level high-frequency wind velocity measurements and a dense 3D representation of the forest was obtained from terrestrial laser scanner data. Wind speed dependence or streamlining was observed for most of the wind directions. Edge effects, i.e. the influence of the here not regarded pressure gradient and the advective terms of the momentum equation, are assumed to cause this heterogeneity. Contrary to the hypothetic shelter effect, which would reduce the drag on sheltered plant parts, the calculated profiles of drag coefficients revealed an increasing CD with PAD (i.e. a dependence on canopy and plant structure).}, note = {SpringerLink; 1612-4669 (Print) 1612-4677 (Online)}, } Applications of flow models to tall plant canopies are limited, amongst other factors, by the lack of detailed information on vegetation structure. A method is presented to record 3D vegetation structure and make this information applicable to the derivation of turbulence parameters suitable for flow models. The relationship between wind speed, drag coefficient (CD) and plant area density (PAD) was experimentally investigated in a mixed conifer forest in the lower part of the Eastern Ore Mountains. Essential information was gathered by collecting multi-level high-frequency wind velocity measurements and a dense 3D representation of the forest was obtained from terrestrial laser scanner data. Wind speed dependence or streamlining was observed for most of the wind directions. Edge effects, i.e. the influence of the here not regarded pressure gradient and the advective terms of the momentum equation, are assumed to cause this heterogeneity. Contrary to the hypothetic shelter effect, which would reduce the drag on sheltered plant parts, the calculated profiles of drag coefficients revealed an increasing CD with PAD (i.e. a dependence on canopy and plant structure). |

## 2010 |

A. Dedner R. Klöfkorn, Nolte; Ohlberger, A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module (Artikel) 2010. @article{1, name = {A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module}, author = {A. Dedner, R. Klöfkorn, M. Nolte, and M. Ohlberger}, editor = {Computing, 90(3-4):165-196.}, year = {2010}, date = {2010-01-01}, abstract = {Starting from an abstract mathematical notion of discrete function spaces and operators, we derive a general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations. Special emphasis is put on concepts for local adaptivity and parallelization with dynamic load balancing. The concepts are based on a corresponding abstract definition of a parallel and hierarchical adaptive grid given in Bastian et al. (Computing 82(2–3):103–119, 2008). Based on the abstract framework, we describe an efficient object oriented implementation of a generic interface for grid-based discretization schemes that is realized in the Dune- Fem library (http://dune.mathematik.uni-freiburg.de). By using interface classes we manage to separate functionality from data structures. Efficiency is obtained by using modern template based generic programming techniques, including static polymorphism, the engine concept, and template metaprogramming.We present numerical results for several benchmark problems and some advanced applications.}, } Starting from an abstract mathematical notion of discrete function spaces and operators, we derive a general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations. Special emphasis is put on concepts for local adaptivity and parallelization with dynamic load balancing. The concepts are based on a corresponding abstract definition of a parallel and hierarchical adaptive grid given in Bastian et al. (Computing 82(2–3):103–119, 2008). Based on the abstract framework, we describe an efficient object oriented implementation of a generic interface for grid-based discretization schemes that is realized in the Dune- Fem library (http://dune.mathematik.uni-freiburg.de). By using interface classes we manage to separate functionality from data structures. Efficiency is obtained by using modern template based generic programming techniques, including static polymorphism, the engine concept, and template metaprogramming.We present numerical results for several benchmark problems and some advanced applications. |

W. Huang L. Kamenski,; Lang, A new anisotropic mesh adaption method based upon hierarchical a posteriori error estimates (Artikel) 2010. (BibTeX) @article{1, name = {A new anisotropic mesh adaption method based upon hierarchical a posteriori error estimates}, author = {W. Huang, L. Kamenski, and J. Lang}, editor = {J. Comput. Phys., 229:2179-2198.}, year = {2010}, date = {2010-01-01}, } |

Ullmann,; Lang, A POD-Galerkin reduced model with updated coefficients for smagorinsky LES (Artikel) 2010. (BibTeX) @article{1, name = {A POD-Galerkin reduced model with updated coefficients for smagorinsky LES}, author = {S. Ullmann and J. Lang}, editor = {In: Proceedings of V. European Conference on Computational Fluid Dynamics , ed. by J.C.F. Pereira and A. Sequeira (Eds.), .}, note = {ECCOMAS CFD 2010 14.-17.06.2010, Lissabon, Portugal}, year = {2010}, date = {2010-01-01}, note = {ECCOMAS CFD 2010 14.-17.06.2010, Lissabon, Portugal}, } |

Gottmeier,; Lang, Adaptive two-step peer methods for thermally coupled incompressible flow (Artikel) 2010. (BibTeX) @article{1, name = {Adaptive two-step peer methods for thermally coupled incompressible flow}, author = {B. Gottmeier and J. Lang}, editor = {In: Proceedings of V. European Conference on Computational Fluid Dynamics , ed. by J.C.F. Pereira and A. Sequeira (Eds.), .}, note = {ECCOMAS CFD 2010 14.-17.06.2010, Lissabon, Portugal}, year = {2010}, date = {2010-01-01}, note = {ECCOMAS CFD 2010 14.-17.06.2010, Lissabon, Portugal}, } |

A. Müller J. Behrens, Giraldo; Wirth, An adaptive discontinuous Galerkin method for modeling cumulus clouds (Artikel) 2010. (BibTeX) @article{1, name = {An adaptive discontinuous Galerkin method for modeling cumulus clouds}, author = {A. Müller, J. Behrens, F. X Giraldo, and V. Wirth}, editor = {Miscellaneous publication.}, note = {(Submitted) In: Fifth European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, 14-17 June 2010, Lisbon, Portugal}, year = {2010}, date = {2010-01-01}, note = {(Submitted) In: Fifth European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, 14-17 June 2010, Lisbon, Portugal}, } |

S Brdar, Dedner; Klöfkorn, CDG Method for Navier-Stokes Equations (Artikel) 2010. (BibTeX) @article{1, name = {CDG Method for Navier-Stokes Equations}, author = {S, Brdar, A. Dedner, and R. Klöfkorn}, editor = {Proc. of the 13th International Conference on Hyperbolic Problems: Theory, Numerics, Applications..}, year = {2010}, date = {2010-01-01}, } |

S. Brdar A. Dedner,; Klöfkorn, Compact and stable Discontinuous Galerkin methods for convection-diffusion problems (Artikel) 2010. (BibTeX) @article{1, name = {Compact and stable Discontinuous Galerkin methods for convection-diffusion problems}, author = {S. Brdar, A. Dedner, and R. Klöfkorn}, editor = {Submitted to: SIAM J. Sci. Comput. 2010.}, year = {2010}, date = {2010-01-01}, } |

Queck, Ronald; Bernhofer, Christian Constructing wind profiles in forests from limited measurements of wind and vegetation structure. (Artikel) 2010. @article{1, name = {Constructing wind profiles in forests from limited measurements of wind and vegetation structure.}, author = {Ronald Queck and Christian Bernhofer}, editor = {Agricultural and Forest Meteorology.}, year = {2010}, date = {2010-01-01}, abstract = {The aim of the advection initiative ADVEX within CarboEurope-IP CEIP was the evaluation of the importance of advection on three coniferous sites. A prerequisite and crucial point for calculating the advective terms of the CO2 balance are the assumptions for the construction of wind fields. Wind measurements have to be interpolated and extrapolated over complex control volumes. Here the plant area density is identified as a key variable. During ADVEX campaigns the rectangular control volumes were marked by four towers at the corners, each carrying four sonic anemometers over the volume height (up to 30 m). A fourth experiment was designed at the CEIP forest site Tharandter Wald to investigate the error made by interpolation between only four measurement levels. 13 sonic anemometers on one tower over the height of 42 m (canopy height is 30m) were installed. In addition profiles of the plant area density were measured to derive plant specific parameterisation of the wind profiles. Profiles of velocity moments and nondimensional wind speed gradients are discussed as basic characteristics of the wind field. A new parameterization scheme for a modified mixing length approach is developed. The model was validated with the high resolved data and applied to calculate horizontal advection for the ADVEX sites. Beside an improvement of the interpolation routine it provides the opportunity to calculate wind profiles having measurements only at two levels, one above and one in the canopy.}, } The aim of the advection initiative ADVEX within CarboEurope-IP CEIP was the evaluation of the importance of advection on three coniferous sites. A prerequisite and crucial point for calculating the advective terms of the CO2 balance are the assumptions for the construction of wind fields. Wind measurements have to be interpolated and extrapolated over complex control volumes. Here the plant area density is identified as a key variable. During ADVEX campaigns the rectangular control volumes were marked by four towers at the corners, each carrying four sonic anemometers over the volume height (up to 30 m). A fourth experiment was designed at the CEIP forest site Tharandter Wald to investigate the error made by interpolation between only four measurement levels. 13 sonic anemometers on one tower over the height of 42 m (canopy height is 30m) were installed. In addition profiles of the plant area density were measured to derive plant specific parameterisation of the wind profiles. Profiles of velocity moments and nondimensional wind speed gradients are discussed as basic characteristics of the wind field. A new parameterization scheme for a modified mixing length approach is developed. The model was validated with the high resolved data and applied to calculate horizontal advection for the ADVEX sites. Beside an improvement of the interpolation routine it provides the opportunity to calculate wind profiles having measurements only at two levels, one above and one in the canopy. |

K. Alexandrov U. Harlander,; Egbers, Definition und Vergleich von Zuständen eines rotierenden Zylinderspalts unter Betrachtung skalenseparierter Strömungsstrukturen (Konferenzbeitrag) in der Strömungsmesstechnik., 18th Fachtagung Lasermethoden (Hrsg.): Seite(n): 50-1, 2010, ISBN: 978-3-9805613-6-5. @inproceedings{1123, name = {Definition und Vergleich von Zuständen eines rotierenden Zylinderspalts unter Betrachtung skalenseparierter Strömungsstrukturen}, author = {K. Alexandrov, U. Harlander, and C. Egbers}, editor = {18th Fachtagung Lasermethoden in der Strömungsmesstechnik.}, isbn = {978-3-9805613-6-5}, year = {2010}, date = {2010-01-01}, pages = {50-1}, abstract = {7-9. September 2010, Cottbus, Germany}, } 7-9. September 2010, Cottbus, Germany |

S. Brinkop V. Grewe, Sausen Stenke Yserentant; Reich, Entwicklung eines Lagrangeschen dynamischen Kerns für Klimamodelle (Artikel) 2010. (BibTeX) @article{1, name = {Entwicklung eines Lagrangeschen dynamischen Kerns für Klimamodelle}, author = {S. Brinkop, V. Grewe, R. Sausen, A. Stenke, H. Yserentant, and S. Reich}, editor = {Unpublished.}, year = {2010}, date = {2010-01-01}, } |

Hertel,; Fröhlich, Error reduction in LES via adaptive moving grids (Artikel) 2010. (BibTeX) @article{1, name = {Error reduction in LES via adaptive moving grids}, author = {C. Hertel and J. Fröhlich}, editor = {In: Quality and Reliability of Large-Eddy Simulations, ed. by M.-V. Salvetti et al. (Hrsg.). Springer, chap. ., pp. ..}, note = {In: QLES II, Pisa, 09.-11.09.2010 In press}, year = {2010}, date = {2010-01-01}, note = {In: QLES II, Pisa, 09.-11.09.2010 In press}, } |

Baumann, Martin; Heuveline, Vincent Evaluation of Different Strategies for Goal Oriented Adaptivity in CFD - Part I: The Stationary Case (Artikel) 2010. (BibTeX) @article{1, name = {Evaluation of Different Strategies for Goal Oriented Adaptivity in CFD - Part I: The Stationary Case}, author = {Martin Baumann and Vincent Heuveline}, editor = {Preprint Series of the Engineering Mathematics and Computing Lab, 2010-05.}, year = {2010}, date = {2010-01-01}, } |

R. Bordás T. Hagemeier,; Thévenin, Experimental Investigation of Droplet-Droplet Interactions (Artikel) 2010. @article{1, name = {Experimental Investigation of Droplet-Droplet Interactions}, author = {R. Bordás, T. Hagemeier, and D. Thévenin}, editor = {In: 23rd European Conference on Liquid Atomization and Spray Systems, pp. 198.1-198.6.}, year = {2010}, date = {2010-01-01}, abstract = {Shadowgraphy is an established imaging measurement method, allowing in particular to determine droplet velocity and diameter distributions. One advantage of Shadowgraphy compared to other non-intrusive measurement methods is its ability to directly observe collision and coalescence processes. As the expected collision probability in many practical two-phase flows is moderate and the acquisition frequency of the Shadowgraphy system is limited, this measurement method must be optimized for the investigation of droplet-droplet interactions. In this work it is shown that Shadowgraphy can be indeed applied to a quantitative investigation of collision events. For this purpose the software (DaVis 7.2 from LaVision) has been considerably improved with the help of its built-in macro language, allowing an automatic analysis of the measurement results. The resulting experimental procedure has been tested using measurements in a two-phase wind tunnel. Corresponding results are compared with available theoretical predictions.}, } Shadowgraphy is an established imaging measurement method, allowing in particular to determine droplet velocity and diameter distributions. One advantage of Shadowgraphy compared to other non-intrusive measurement methods is its ability to directly observe collision and coalescence processes. As the expected collision probability in many practical two-phase flows is moderate and the acquisition frequency of the Shadowgraphy system is limited, this measurement method must be optimized for the investigation of droplet-droplet interactions. In this work it is shown that Shadowgraphy can be indeed applied to a quantitative investigation of collision events. For this purpose the software (DaVis 7.2 from LaVision) has been considerably improved with the help of its built-in macro language, allowing an automatic analysis of the measurement results. The resulting experimental procedure has been tested using measurements in a two-phase wind tunnel. Corresponding results are compared with available theoretical predictions. |

Horenko, Finite element approach to clustering of multidimensional time series (Artikel) 2010. (BibTeX) @article{1, name = {Finite element approach to clustering of multidimensional time series}, author = {I. Horenko}, editor = {SIAM J. of Sci. Comp., 32(1):62-83.}, year = {2010}, date = {2010-01-01}, } |

I. Bastigkeit R. Fischer, Leitl; Schatzmann, Fundamental quality requirements for the generation of LES specific validation data sets from systematic wind tunnel model experiments (Artikel) 2010. (BibTeX) @article{2, name = {Fundamental quality requirements for the generation of LES specific validation data sets from systematic wind tunnel model experiments}, author = {I. Bastigkeit, R. Fischer, B. Leitl, and M. Schatzmann}, editor = {Proceedings of CWE 2010.}, year = {2010}, date = {2010-01-01}, } |

R. Fischer I. Bastigkeit, Leitl; Schatzmann, Generation of spatio-temporally high resolved datasets for the validation of LES-models simulating flow and dispersion phenomena within the lower atmospheric boundary layer (Artikel) 2010. (BibTeX) @article{1, name = {Generation of spatio-temporally high resolved datasets for the validation of LES-models simulating flow and dispersion phenomena within the lower atmospheric boundary layer}, author = {R. Fischer, I. Bastigkeit, B. Leitl, and M. Schatzmann}, editor = {Proceedings of CWE 2010.}, year = {2010}, date = {2010-01-01}, } |

Achatz,; Klein,; Senf, Gravity waves, scale asymptotics, and the pseudo-incompressible equations (Artikel) Journal of Fluid Mechanics,, 663:120-147., 2010. @article{663:120-147, name = {Gravity waves, scale asymptotics, and the pseudo-incompressible equations}, author = {U. Achatz and R. Klein and F. Senf}, year = {2010}, date = {2010-05-25}, journal = {Journal of Fluid Mechanics,}, volume = {663:120-147.}, abstract = {Multiple-scale asymptotics is used to analyze the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As small expansion parameter the ratio of inverse of the vertical wave number and potential temperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic gravity waves, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak strati cation is adopted. To describe vertical propagation of wave packets over several atmospheric scale heights, WKB theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justi cation for the use of the pseudo-incompressible equations for studies of gravity-wave breaking in the atmosphere for arbitrary background strati cation. The WKB theory interestingly also holds at wave amplitudes close to static instability. In the mean-flow equations we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical-momentum equation which cannot be obtained from Boussinesq or anelastic dynamics.}, } Multiple-scale asymptotics is used to analyze the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As small expansion parameter the ratio of inverse of the vertical wave number and potential temperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic gravity waves, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak strati cation is adopted. To describe vertical propagation of wave packets over several atmospheric scale heights, WKB theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justi cation for the use of the pseudo-incompressible equations for studies of gravity-wave breaking in the atmosphere for arbitrary background strati cation. The WKB theory interestingly also holds at wave amplitudes close to static instability. In the mean-flow equations we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical-momentum equation which cannot be obtained from Boussinesq or anelastic dynamics. |

M. Baumann V. Heuveline,; et al, Hiflow3 - A Flexible and Hardware-Aware Parallel Finite Element Package (Artikel) 2010. (BibTeX) @article{1, name = {Hiflow3 - A Flexible and Hardware-Aware Parallel Finite Element Package}, author = {M. Baumann, V. Heuveline, and et al}, editor = {Parallel/High-Performance Object-Oriented Scientific Computing (POOSC'10).}, year = {2010}, date = {2010-01-01}, } |

Tack, Large Eddy Simulation horizontaler Konvektionswalzen in der atmosphärischen Grenzschicht (Artikel) 2010. (BibTeX) @article{1, name = {Large Eddy Simulation horizontaler Konvektionswalzen in der atmosphärischen Grenzschicht}, author = {A. Tack}, editor = {Miscellaneous publication, Interner Bericht.}, note = {Institut für Strömungsmechanik, TU Dresden, in Kooperation mit dem Finnischen Meteorologischen Institut (FMI).}, year = {2010}, date = {2010-01-01}, note = {Institut für Strömungsmechanik, TU Dresden, in Kooperation mit dem Finnischen Meteorologischen Institut (FMI).}, } |

Hertel,; Fröhlich, Large-Eddy Simulation with adaptive refinement for the flow over periodic hills (Artikel) 2010. (BibTeX) @article{1, name = {Large-Eddy Simulation with adaptive refinement for the flow over periodic hills}, author = {C. Hertel and J. Fröhlich}, editor = {DLES, 8.}, note = {07.-09.07.2010, Eindhoven, Niederlande, in press}, year = {2010}, date = {2010-01-01}, note = {07.-09.07.2010, Eindhoven, Niederlande, in press}, } |

S. Jebens O. Knoth, Arnold; Weiner, Linearly implicit peer methods for the compressible Euler equations (Artikel) 2010. (BibTeX) @article{1, name = {Linearly implicit peer methods for the compressible Euler equations}, author = {S. Jebens, O. Knoth, M. Arnold, and R. Weiner}, editor = {Applied Numerical Mathematics.}, year = {2010}, date = {2010-01-01}, } |

D. Ruprecht R. Klein,; Majda, Modulation of Internal Gravity Waves in a Multiscale Model for Deep Convection on Mesoscales (Artikel) 2010. @article{1, name = {Modulation of Internal Gravity Waves in a Multiscale Model for Deep Convection on Mesoscales}, author = {D. Ruprecht, R. Klein, and A. J Majda}, editor = {Journal of Atmospheric Sciences, 67(8):2504-2519.}, year = {2010}, date = {2010-01-01}, abstract = {Starting from the conservation laws for mass, momentum, and energy together with a three species, bulk micro-physics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multi-scale asymptotic techniques. From the leading order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime which the analysis is based on. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and micro-scale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and non-saturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: it (i) reduces vertical energy transport by waves, (ii) increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) introduces a new lower horizontal cut-off wavenumber besides the well-known high wavenumber cut-off, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime.}, } Starting from the conservation laws for mass, momentum, and energy together with a three species, bulk micro-physics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multi-scale asymptotic techniques. From the leading order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime which the analysis is based on. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and micro-scale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and non-saturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: it (i) reduces vertical energy transport by waves, (ii) increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) introduces a new lower horizontal cut-off wavenumber besides the well-known high wavenumber cut-off, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime. |

M. Schlegel O. Knoth, Arnold; Wolke, Numerical solution of multiscale problems in atmospheric modeling (Artikel) 2010. (BibTeX) @article{1, name = {Numerical solution of multiscale problems in atmospheric modeling}, author = {M. Schlegel, O. Knoth, M. Arnold, and R. Wolke}, editor = {Applied Numerical Mathematics.}, year = {2010}, date = {2010-01-01}, } |

Horenko, On clustering of non-stationary meteorological time series (Artikel) 2010. @article{1, name = {On clustering of non-stationary meteorological time series}, author = {I. Horenko}, editor = {Dynamics of Atmospheres and Oceans, 49(2-3):164-187.}, year = {2010}, date = {2010-01-01}, abstract = {A method for clustering of multidimensional non-stationary meteorological time series is presented. The approach is based on optimization of the regularized averaged clustering functional describing the quality of data representation in terms of several regression models and a metastable hidden process switching between them. Proposed numerical clustering algorithm is based on application of the finite element method (FEM) to the problem of non-stationary time series analysis. The main advantage of the presented algorithm compared to Hidden Markov Models (HMMs) and to finite mixture models is that no a priori assumptions about the probability model for the hidden and observed processes (e.g., Markovianity or stationarity) are necessary for the proposed method. Another attractive numerical feature of the discussed algorithm is the possibility to choose the optimal number of metastable clusters and a natural opportunity to control the fuzziness of the resulting decomposition a posteriory, based on the statistical distinguishability of the resulting persistent cluster states. The resulting FEM-K-trends algorithm is compared with some standard fuzzy clustering methods on toy model examples and on analysis of multidimensional historical temperature data locally in Europe and on the global temperature data set.}, } A method for clustering of multidimensional non-stationary meteorological time series is presented. The approach is based on optimization of the regularized averaged clustering functional describing the quality of data representation in terms of several regression models and a metastable hidden process switching between them. Proposed numerical clustering algorithm is based on application of the finite element method (FEM) to the problem of non-stationary time series analysis. The main advantage of the presented algorithm compared to Hidden Markov Models (HMMs) and to finite mixture models is that no a priori assumptions about the probability model for the hidden and observed processes (e.g., Markovianity or stationarity) are necessary for the proposed method. Another attractive numerical feature of the discussed algorithm is the possibility to choose the optimal number of metastable clusters and a natural opportunity to control the fuzziness of the resulting decomposition a posteriory, based on the statistical distinguishability of the resulting persistent cluster states. The resulting FEM-K-trends algorithm is compared with some standard fuzzy clustering methods on toy model examples and on analysis of multidimensional historical temperature data locally in Europe and on the global temperature data set. |

Horenko,; Schütte, On Metastable Conformational Analysis of Nonequilibrium Biomolecular Time Series (Artikel) 2010. (BibTeX) @article{1, name = {On Metastable Conformational Analysis of Nonequilibrium Biomolecular Time Series}, author = {I. Horenko and C. Schütte}, editor = {Multiscale Modeling & Simulation, 8(2):701-716.}, year = {2010}, date = {2010-01-01}, } |

Horenko, On the Identification of Nonstationary Factor Models and Their Application to Atmospheric Data Analysis (Artikel) 2010. @article{1, name = {On the Identification of Nonstationary Factor Models and Their Application to Atmospheric Data Analysis}, author = {I. Horenko}, editor = {Journal of Atmospheric Sciences, 67(5):1559-1574 .}, year = {2010}, date = {2010-01-01}, abstract = {A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences.}, } A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences. |

D. Hertwig B. Leitl,; Schatzmann, Organized turbulent structures –- The link between experimental data and LES modeling (Artikel) 2010. (BibTeX) @article{1, name = {Organized turbulent structures –- The link between experimental data and LES modeling}, author = {D. Hertwig, B. Leitl, and M. Schatzmann}, editor = {Proceedings of CWE 2010.}, year = {2010}, date = {2010-01-01}, } |

Horenko, Parameter identification in nonstationary Markov chains with external impact and its application to computational sociology (Artikel) 2010. (BibTeX) @article{1, name = {Parameter identification in nonstationary Markov chains with external impact and its application to computational sociology}, author = {I. Horenko}, editor = {Multiscale Modeling & Simulation.}, year = {2010}, date = {2010-01-01}, } |

L. Putzig I. Horenko,; Metzner, Persistent BV-clustering of non-stationary time series and its application to analysis of financial and biological data (Artikel) 2010. (BibTeX) @article{1, name = {Persistent BV-clustering of non-stationary time series and its application to analysis of financial and biological data}, author = {L. Putzig, I. Horenko, and P. Metzner}, editor = {in preparation.}, year = {2010}, date = {2010-01-01}, } |

A. Bienert R. Stiel, Queck; Maas, Photogrammetrische Bestimmung von statischen und dynamischen Verformungsstrukturen an Einzelbäumen (Artikel) 2010. @article{1, name = {Photogrammetrische Bestimmung von statischen und dynamischen Verformungsstrukturen an Einzelbäumen}, author = {A. Bienert, R. Stiel, H.-G. Queck, and Maas}, editor = {Allgemeine Vermessungs-Nachrichten, 5:190-197.}, year = {2010}, date = {2010-01-01}, abstract = {Der Beitrag befasst sich mit der Bestimmung und Analyse von statischen und dynamischen Verformungsstrukturen an Einzelbäumen. Dazu wurden zum einen terrestrische Laserscannerdaten verwendet, indem ein Baum im unbelasteten Zustand und während einer simulierten statischen Deformation aufgenommen wurde. Die Verformungsstruktur des Baumes wurde anschließend durch Analysen in den 3D-Punktwolken bestimmt. In einem zweiten Ansatz wurde eine natürlich induzierte sowie windinduzierte dynamische Betrachtung durch Tracking markanter Bildpunkte in Bildsequenzen einer Kamera realisiert, wobei die 2D-Trajektorien das zeitliche Verformungsverhalten wiedergeben. Die Resultate bilden eine Voraussetzung für mechanische Untersuchungen hinsichtlich maximaler Windlasten sowie für Forschungsarbeiten zu turbulenten Strömungen und zur Analyse von Gasaustauschprozessen in Baumbeständen.}, } Der Beitrag befasst sich mit der Bestimmung und Analyse von statischen und dynamischen Verformungsstrukturen an Einzelbäumen. Dazu wurden zum einen terrestrische Laserscannerdaten verwendet, indem ein Baum im unbelasteten Zustand und während einer simulierten statischen Deformation aufgenommen wurde. Die Verformungsstruktur des Baumes wurde anschließend durch Analysen in den 3D-Punktwolken bestimmt. In einem zweiten Ansatz wurde eine natürlich induzierte sowie windinduzierte dynamische Betrachtung durch Tracking markanter Bildpunkte in Bildsequenzen einer Kamera realisiert, wobei die 2D-Trajektorien das zeitliche Verformungsverhalten wiedergeben. Die Resultate bilden eine Voraussetzung für mechanische Untersuchungen hinsichtlich maximaler Windlasten sowie für Forschungsarbeiten zu turbulenten Strömungen und zur Analyse von Gasaustauschprozessen in Baumbeständen. |

L.G.M. de Souza G. Janiga, John; Thévenin, Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm (Artikel) 2010. @article{1, name = {Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm}, author = {L.G.M. de Souza, G. Janiga, V. John, and D. Thévenin}, editor = {Chemical Engineering Science, 65(9):2741-2750.}, year = {2010}, date = {2010-01-01}, abstract = {An adaptive algorithm suitable for reconstructing a distribution when knowing only a small number of its moments is presented. This method elaborates on a previous technique presented in John et al. (2007), but leads to many advantages compared with the original algorithm. The so-called “finite moment problem” arises in many fields of science, but is particularly important for particulate flows in chemical engineering. Up to now, there is no well-established algorithm available to solve this problem. The examples considered in this work come from crystallization processes. For such applications, it is of crucial interest to reconstruct the particle size distributions (PSD) knowing only a small number of its moments, obtained mostly from numerical simulations or from advanced experiments, but without any a priori knowledge concerning the shape of this PSD. This was already possible in many cases with the original algorithm of John et al. (2007), but complex shapes could not be identified appropriately. The key of the advanced algorithm is the adaptive criterion for positioning dynamically the nodes in an appropriate manner. It turns out that the adaptive algorithm shows considerable improvements in the reconstruction of distributions with a quickly changing curvature or for non-smooth distributions. Since such configurations are quite often found in practice, the new algorithm is more widely applicable compared with the original method.}, } An adaptive algorithm suitable for reconstructing a distribution when knowing only a small number of its moments is presented. This method elaborates on a previous technique presented in John et al. (2007), but leads to many advantages compared with the original algorithm. The so-called “finite moment problem” arises in many fields of science, but is particularly important for particulate flows in chemical engineering. Up to now, there is no well-established algorithm available to solve this problem. The examples considered in this work come from crystallization processes. For such applications, it is of crucial interest to reconstruct the particle size distributions (PSD) knowing only a small number of its moments, obtained mostly from numerical simulations or from advanced experiments, but without any a priori knowledge concerning the shape of this PSD. This was already possible in many cases with the original algorithm of John et al. (2007), but complex shapes could not be identified appropriately. The key of the advanced algorithm is the adaptive criterion for positioning dynamically the nodes in an appropriate manner. It turns out that the adaptive algorithm shows considerable improvements in the reconstruction of distributions with a quickly changing curvature or for non-smooth distributions. Since such configurations are quite often found in practice, the new algorithm is more widely applicable compared with the original method. |

R. Klein U. Achatz, Bresch; Knio, Regime of Validity of Sound-Proof Atmospheric Flow Models (Artikel) 2010. @article{1, name = {Regime of Validity of Sound-Proof Atmospheric Flow Models}, author = {R. Klein, U. Achatz, D. Bresch, and O. Knio}, editor = {Journal of the Atmospheric Sciences.}, year = {2010}, date = {2010-01-01}, abstract = {Ogura and Phillips (1962) derived the original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. To arrive at a reduced model which would simultaneously represent internal gravity waves and the effects of advection on the same time scale they had to adopt a distinguished limit stating that the dimensionless stability of the background state be of the order of the Mach number squared. For typical flow Mach numbers of M ~ 1/30 this amounts to total variations of potential temperature across the troposphere of less than one Kelvin, i.e., to unrealistically weak stratification. Various generalizations of the original anelastic model have been proposed to remedy this issue, e.g., by Dutton & Fichtl (1969), and Lipps & Hemler (1982). Durran (1989) proposed the pseudo-incompressible model following the same goals, but a somewhat different route of argumentation. The present paper provides a scale analysis showing that the regime of validity of two of these extended models covers stratification strengths of order (hsc/θ) dθ/dz < M2/3 which corresponds to realistic variations of potential temperature, θ, across the pressure scale height, hsc, of (see PDF for full equation). Specifically, it is shown that: (i) for (hsc/θ) dθ/dz < Mμ with 0 < μ < 2 the atmosphere features three asymptotically distinct time scales, namely those of advection, internal gravity waves, and sound waves; (ii) within this range of stratifications the structures and frequencies of the linearized internal wave modes of the compressible, anelastic, and pseudo-incompressible models agree up to order Mμ; and (iii) if μ < 2/3, the accumulated phase differences of internal waves remain asymptotically small even over the long advective time scale. The argument is completed by observing that the three models agree with respect to the advective nonlinearities, and that all other nonlinear terms are of higher order in M.}, } Ogura and Phillips (1962) derived the original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. To arrive at a reduced model which would simultaneously represent internal gravity waves and the effects of advection on the same time scale they had to adopt a distinguished limit stating that the dimensionless stability of the background state be of the order of the Mach number squared. For typical flow Mach numbers of M ~ 1/30 this amounts to total variations of potential temperature across the troposphere of less than one Kelvin, i.e., to unrealistically weak stratification. Various generalizations of the original anelastic model have been proposed to remedy this issue, e.g., by Dutton & Fichtl (1969), and Lipps & Hemler (1982). Durran (1989) proposed the pseudo-incompressible model following the same goals, but a somewhat different route of argumentation. The present paper provides a scale analysis showing that the regime of validity of two of these extended models covers stratification strengths of order (hsc/θ) dθ/dz < M2/3 which corresponds to realistic variations of potential temperature, θ, across the pressure scale height, hsc, of (see PDF for full equation). Specifically, it is shown that: (i) for (hsc/θ) dθ/dz < Mμ with 0 < μ < 2 the atmosphere features three asymptotically distinct time scales, namely those of advection, internal gravity waves, and sound waves; (ii) within this range of stratifications the structures and frequencies of the linearized internal wave modes of the compressible, anelastic, and pseudo-incompressible models agree up to order Mμ; and (iii) if μ < 2/3, the accumulated phase differences of internal waves remain asymptotically small even over the long advective time scale. The argument is completed by observing that the three models agree with respect to the advective nonlinearities, and that all other nonlinear terms are of higher order in M. |

Dedner,; Klöfkorn, Stabilization for discontinuous Galerkin methods applied to systems of conservation laws (Artikel) 2010. (BibTeX) @article{1, name = {Stabilization for discontinuous Galerkin methods applied to systems of conservation laws}, author = {A. Dedner and R. Klöfkorn}, editor = {In: Hyperbolic problems. Theory, numerics and applications. Plenary and invited talks. Proceedings of the 12th international conference on hyperbolic problems, ed. by Tadmor, E., Liu, J.G., Tzavaras, A.E. American Mathematical Society, chap. ., pp. 253-268 .}, year = {2010}, date = {2010-01-01}, } |

Wirth, The dynamics of orographic banner clouds (Artikel) 2010. (BibTeX) @article{1, name = {The dynamics of orographic banner clouds}, author = {V. Wirth}, editor = {In: The 90th American Meteorological Society Annual Meeting, Atlanta, GA, USA and Miscellaneous publication.}, year = {2010}, date = {2010-01-01}, } |

L. Scheck S. Jones,; Juckes, The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model - Part I: Zonally-oriented front (Artikel) 2010. (BibTeX) @article{1, name = {The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model - Part I: Zonally-oriented front}, author = {L. Scheck, S. Jones, and Juckes}, editor = {JAS.}, note = {to appear 2011}, year = {2010}, date = {2010-01-01}, note = {to appear 2011}, } |

L. Scheck S. Jones,; Juckes, The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model - Part II: Frontal waves (Artikel) 2010. (BibTeX) @article{1, name = {The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model - Part II: Frontal waves}, author = {L. Scheck, S. Jones, and Juckes}, editor = {JAS.}, note = {to appear 2011}, year = {2010}, date = {2010-01-01}, note = {to appear 2011}, } |

R. Queck A. Bienert,; Eipper, Turbulente Austauschprozesse zwischen Waldflächen und der Atmosphäre (Artikel) 2010. @article{1, name = {Turbulente Austauschprozesse zwischen Waldflächen und der Atmosphäre}, author = {R. Queck, A. Bienert, and T. Eipper}, editor = {Miscellaneous publication, Fernsehbeitrag des ARD in der Sendung [W] wie Wissen, http://www.daserste.de/wwiewissen/vorschau.asp..}, year = {2010}, date = {2010-01-01}, abstract = {Darstellung der Arbeiten im Rahmen des Forschungsprojektes "Turbulente Austauschprozesse zwischen Waldflächen und der Atmosphäre" an der TU-Dresden. In Schlichter, A.: "Sturmsicherer Wald"}, } Darstellung der Arbeiten im Rahmen des Forschungsprojektes "Turbulente Austauschprozesse zwischen Waldflächen und der Atmosphäre" an der TU-Dresden. In Schlichter, A.: "Sturmsicherer Wald" |

T. von Larcher U. Harlander,; Egbers, Untersuchungen von Welleninteraktionen in einer thermisch getriebenen, rotierenden Zylinderspaltströmung mittels LDA und Thermographie (Artikel) 2010, ISBN: 978-3-9805613-6-5. (BibTeX) @article{1, name = {Untersuchungen von Welleninteraktionen in einer thermisch getriebenen, rotierenden Zylinderspaltströmung mittels LDA und Thermographie}, author = {T. von Larcher, U. Harlander, and C. Egbers}, editor = {In: 18. GALA-Fachtagung Lasermethoden in der Strömungsmesstechnik, ed. by C. Egbers, B. Ruck, A. Leder, D. Dopheide.}, note = {7.-9. September 2010, Cottbus ISBN: 978-3-9805613-6-5}, isbn = {978-3-9805613-6-5}, year = {2010}, date = {2010-01-01}, note = {7.-9. September 2010, Cottbus ISBN: 978-3-9805613-6-5}, } |

A. Bienert K. Pech,; Maas, Verfahren zur Registrierung von Laserscannerdaten in Waldbeständen (Artikel) 2010. @article{1, name = {Verfahren zur Registrierung von Laserscannerdaten in Waldbeständen}, author = {A. Bienert, K. Pech, and H.G. Maas}, editor = {Schweizerische Zeitschrift für Forstwesen, 162(6):178-185.}, year = {2010}, date = {2010-01-01}, abstract = {Laser scanning is a fast and efficient 3-D measurement technique to capture surface points describing the geometry of a complex object in an accurate and reliable way. Besides airborne laser scanning, terrestrial laser scanning finds growing interest for forestry applications. These two different recording platforms show large differences in resolution, recording area and scan viewing direction. Using both datasets for a combined point cloud analysis may yield advantages because of their largely complementary information. In this paper, methods will be presented to automatically register airborne and terrestrial laser scanner point clouds of a forest stand. In a first step, tree detection is performed in both datasets in an automatic manner. In a second step, corresponding tree positions are determined using RANSAC. Finally, the geometric transformation is performed, divided in a coarse and fine registration. After a coarse registration, the fine registration is done in an iterative manner (ICP) using the point clouds itself. The methods are tested and validated with a dataset of a forest stand. The presented registration results provide accuracies which fulfill the forestry requirements.}, } Laser scanning is a fast and efficient 3-D measurement technique to capture surface points describing the geometry of a complex object in an accurate and reliable way. Besides airborne laser scanning, terrestrial laser scanning finds growing interest for forestry applications. These two different recording platforms show large differences in resolution, recording area and scan viewing direction. Using both datasets for a combined point cloud analysis may yield advantages because of their largely complementary information. In this paper, methods will be presented to automatically register airborne and terrestrial laser scanner point clouds of a forest stand. In a first step, tree detection is performed in both datasets in an automatic manner. In a second step, corresponding tree positions are determined using RANSAC. Finally, the geometric transformation is performed, divided in a coarse and fine registration. After a coarse registration, the fine registration is done in an iterative manner (ICP) using the point clouds itself. The methods are tested and validated with a dataset of a forest stand. The presented registration results provide accuracies which fulfill the forestry requirements. |

A. Bienert R. Queck, Schmidt Bernhofer; Maas, Voxel space analysis of terrestrial laser scans in forests for wind field modelling (Artikel) 2010. (BibTeX) @article{1, name = {Voxel space analysis of terrestrial laser scans in forests for wind field modelling}, author = {A. Bienert, R. Queck, A. Schmidt, C. Bernhofer, and H.-G. Maas}, editor = {International Archives of Photogrammetry.Remote Sensing and Spatial Information Sciences, 38(5):92-97.}, year = {2010}, date = {2010-01-01}, } |

## 2009 |

R. Bordas K. Hanke, Bencs; Thévenin, 2D-PIV Measurements in a Two-Phase Wind Tunnel Normal to the Main Flow (Artikel) 2009. (BibTeX) @article{1, name = {2D-PIV Measurements in a Two-Phase Wind Tunnel Normal to the Main Flow}, author = {R. Bordas, K. Hanke, P. Bencs, and D. Thévenin}, editor = {Miscellaneous publication.}, year = {2009}, date = {2009-01-01}, } |

S. Hickel D.A. von Terzi,; Fröhlich, An adaptive local deconvolution method for general curvilinear coordinate systems (Artikel) 2009. (BibTeX) @article{1, name = {An adaptive local deconvolution method for general curvilinear coordinate systems}, author = {S. Hickel, D.A. von Terzi, and J. Fröhlich}, editor = {European Turbulence Conference.}, note = {07.-10.09.2009, Marburg, Deutschland}, year = {2009}, date = {2009-01-01}, note = {07.-10.09.2009, Marburg, Deutschland}, } |

J. P Mellado B. Stevens, Schmidt; Peters, Analysis of latent heat effects in the cloud-top mixing layer (Artikel) 2009. (BibTeX) @article{1, name = {Analysis of latent heat effects in the cloud-top mixing layer}, author = {J. P Mellado, B. Stevens, H. Schmidt, and N. Peters}, editor = {Quarterly Journal of the Royal Meteorological Society, 135(641):963-978.}, year = {2009}, date = {2009-01-01}, } |

Juan P Mellado Heiko Schmidt, Bjorn Stevens; Peters, Norbert Analysis of the cloud top mixing layer using DNS (Artikel) 2009. @article{1, name = {Analysis of the cloud top mixing layer using DNS}, author = {Juan P Mellado, Heiko Schmidt, Bjorn Stevens, and Norbert Peters}, editor = {In: The Sixth International Symposium on Turbulence and Shear Flow, Seoul, Korea .}, year = {2009}, date = {2009-01-01}, abstract = {It has been recognized during the last decades that cloud effects remain one of the largest sources of uncertainty in model-based estimates of climate sensitivity, and in particular entrainment rates in stratocumulus-topped mixed layers need urgently better models (Stevens, 2002) in order to improve predictions obtained with large-scale approaches, like large-eddy simulations. Cloud-top mixed layers, and in particular the possibility of an entrainment instability appearing at the top of the cloud deck due to buoyancy reversal created by evaporative cooling when the upper subsaturated and hot subsiding air mixes with the lower moist and colder layer, have received considerable attention (Lilly, 1968, Randall, 1980, Kuo and Schubert, 1988, Yamaguchi and Randall, 2008), and even small-scale analysis via laboratory experiments and numerical simulations have been presented (Shy and Breidenthal, 1990, Siems et al., 1990, Siems and Bretherton, 1992). This work continues the study of the cloud-top mixing layer on a small-scale using direct numerical simulation (DNS) in order to improve the understanding of the phenomena taking place at this region, and ultimately derive better entrainment models. The idealized configuration considered here is a two-layer system, the upper layer hot and subsaturated and the lower cold and saturated, with or without shear.}, } It has been recognized during the last decades that cloud effects remain one of the largest sources of uncertainty in model-based estimates of climate sensitivity, and in particular entrainment rates in stratocumulus-topped mixed layers need urgently better models (Stevens, 2002) in order to improve predictions obtained with large-scale approaches, like large-eddy simulations. Cloud-top mixed layers, and in particular the possibility of an entrainment instability appearing at the top of the cloud deck due to buoyancy reversal created by evaporative cooling when the upper subsaturated and hot subsiding air mixes with the lower moist and colder layer, have received considerable attention (Lilly, 1968, Randall, 1980, Kuo and Schubert, 1988, Yamaguchi and Randall, 2008), and even small-scale analysis via laboratory experiments and numerical simulations have been presented (Shy and Breidenthal, 1990, Siems et al., 1990, Siems and Bretherton, 1992). This work continues the study of the cloud-top mixing layer on a small-scale using direct numerical simulation (DNS) in order to improve the understanding of the phenomena taking place at this region, and ultimately derive better entrainment models. The idealized configuration considered here is a two-layer system, the upper layer hot and subsaturated and the lower cold and saturated, with or without shear. |

Klein, Rupert Asymptotics, structure, and integration of sound-proof atmospheric flow equations (Artikel) 2009. (BibTeX) @article{1, name = {Asymptotics, structure, and integration of sound-proof atmospheric flow equations}, author = {Rupert Klein}, editor = {Theoretical and Computational Fluid Dynamics, 23(3):161-195.}, year = {2009}, date = {2009-01-01}, } |

Juan P Mellado Bjorn Stevens, Heiko Schmidt; Peters, Norbert Buoyancy reversal in the cloud-top mixing layer (Artikel) 2009. @article{1, name = {Buoyancy reversal in the cloud-top mixing layer}, author = {Juan P Mellado, Bjorn Stevens, Heiko Schmidt, and Norbert Peters}, editor = {Miscellaneous publication, 4th IMS Turbulence Workshop, Imperial College, London.}, year = {2009}, date = {2009-01-01}, abstract = {Results from theoretical and numerical studies of the cloud-top mixing layer with buoyancy reversal due to evaporative cooling in a small size system (of the order of 10 m) will be presented. An ideal two-layer configuration has been defined following previous literature and a linear stability analysis has been performed, showing the buoyancy reversal instability and providing a reinterpretation of the buoyancy reversal parameter D in terms of the ratio between the stable and the unsatble time-scales. A high-order numerical scheme has been employed to investigate the nonlinear regime, and results suggest that a turbulent state in the lower layer can develop from this instability for cases D << 1 typical of stratocumuli, without additional external forcing. Three-dimensional simulations confirm this result. It is also observed that mixing with the upper layer occurs mainly through laminar diffusion, without engulfing pure upper fluid, and the turbulent lower layer is capped by the inversion. Characterization of the resulting turbulent fields from three-dimensional simulations is currently in progress.}, } Results from theoretical and numerical studies of the cloud-top mixing layer with buoyancy reversal due to evaporative cooling in a small size system (of the order of 10 m) will be presented. An ideal two-layer configuration has been defined following previous literature and a linear stability analysis has been performed, showing the buoyancy reversal instability and providing a reinterpretation of the buoyancy reversal parameter D in terms of the ratio between the stable and the unsatble time-scales. A high-order numerical scheme has been employed to investigate the nonlinear regime, and results suggest that a turbulent state in the lower layer can develop from this instability for cases D << 1 typical of stratocumuli, without additional external forcing. Three-dimensional simulations confirm this result. It is also observed that mixing with the upper layer occurs mainly through laminar diffusion, without engulfing pure upper fluid, and the turbulent lower layer is capped by the inversion. Characterization of the resulting turbulent fields from three-dimensional simulations is currently in progress. |

R. Queck A. Bienert,; Harmansa, Calculating advective fluxes in tall canopies – Towards better wind speed distribution using 3D vegetation scans in high resolution. (Konferenz) 2009. @conference{1, name = {Calculating advective fluxes in tall canopies – Towards better wind speed distribution using 3D vegetation scans in high resolution.}, author = {R. Queck, A. Bienert, and S. Harmansa}, editor = {In: Konferenzbeitrag.}, note = {Atmospheric Transport and Chemistry in Forest Ecosystems, Castle of Thurnau, Oct 5 - 8, 2009.}, year = {2009}, date = {2009-10-05}, abstract = {The wind speed distribution in forests is dominated by inhomogeneities like step changes in stand height and forest clearings. Thus a major limitation in the attempts to describe and model the wind field in destined tall canopies is the parameterization of plant architecture. The relationship between wind speed, drag coefficient and plant area distribution was experimentally investigated in a mixed conifer forests in the lower ranges of the Osterzgebirge. The results of this study will be applied to different kinds of flow models to investigate the influence of advective fluxes of energy and matter. From May 2008 to May 2009 intensive turbulence measurements took place on a transect over the forest clearing „Wildacker“ (Tharandter Wald, N 50°57'49", E 13°34'01"). In total 25 measurement points, at 4 towers (heights: 40m, 40m, 40m, 30m) including five at ground level position (2 m), are used to record the turbulent flow simultaneously. Terrestrial laser scanning is a fast developing tool and appears to be an efficient method to record 3D models of the vegetation. The forest stands around the clearing (500 m x 60 m) were scanned applying a Riegl LMS-Z 420i and a Faro LSHE880. Thereby scans from different ground positions and from the top of the main tower (height: 40m) were done. The scans were filtered and combined to a single 3D representation of the stands. The detection of trees was done automatically and mean tree distances were calculated. The 3D point cloud of trees in a 60m x 310m x 50m model domain was transformed into a 3D voxel space. The normalized point density of each voxel represents the plant area density PAD. A scaling of the laser derived totals per floor space was done by measurements with the LAI2000 (LICOR). The so calculated PAD and the spatial arrangement of points inside the voxel can be used to derive a parameterization for the drag coefficients. Simultaneously, the drag coefficients are calculated from turbulence measurements at the positions of anemometers. Finally the dependency between drag coefficients and PAD can be investigated with respect to stability and wind speed. Using measured wind profiles this study aims further to validate and develop estimates of parameters like mixing length, displacement height and roughness length from the plant area density profile.}, note = {Atmospheric Transport and Chemistry in Forest Ecosystems, Castle of Thurnau, Oct 5 - 8, 2009.}, } The wind speed distribution in forests is dominated by inhomogeneities like step changes in stand height and forest clearings. Thus a major limitation in the attempts to describe and model the wind field in destined tall canopies is the parameterization of plant architecture. The relationship between wind speed, drag coefficient and plant area distribution was experimentally investigated in a mixed conifer forests in the lower ranges of the Osterzgebirge. The results of this study will be applied to different kinds of flow models to investigate the influence of advective fluxes of energy and matter. From May 2008 to May 2009 intensive turbulence measurements took place on a transect over the forest clearing „Wildacker“ (Tharandter Wald, N 50°57'49", E 13°34'01"). In total 25 measurement points, at 4 towers (heights: 40m, 40m, 40m, 30m) including five at ground level position (2 m), are used to record the turbulent flow simultaneously. Terrestrial laser scanning is a fast developing tool and appears to be an efficient method to record 3D models of the vegetation. The forest stands around the clearing (500 m x 60 m) were scanned applying a Riegl LMS-Z 420i and a Faro LSHE880. Thereby scans from different ground positions and from the top of the main tower (height: 40m) were done. The scans were filtered and combined to a single 3D representation of the stands. The detection of trees was done automatically and mean tree distances were calculated. The 3D point cloud of trees in a 60m x 310m x 50m model domain was transformed into a 3D voxel space. The normalized point density of each voxel represents the plant area density PAD. A scaling of the laser derived totals per floor space was done by measurements with the LAI2000 (LICOR). The so calculated PAD and the spatial arrangement of points inside the voxel can be used to derive a parameterization for the drag coefficients. Simultaneously, the drag coefficients are calculated from turbulence measurements at the positions of anemometers. Finally the dependency between drag coefficients and PAD can be investigated with respect to stability and wind speed. Using measured wind profiles this study aims further to validate and develop estimates of parameters like mixing length, displacement height and roughness length from the plant area density profile. |

E Audusse R Klein,; Owinoh, Conservative Discretization of Coriolis Force (Artikel) 2009. @article{22, name = {Conservative Discretization of Coriolis Force}, author = {E Audusse, R Klein, and A Z Owinoh}, year = {2009}, date = {2009-01-01}, abstract = {J. Comput. Phys, 228(8):2934-2950.}, } J. Comput. Phys, 228(8):2934-2950. |

M. Giorgetta T. Hundertmark, Korn Reich; Restelli, Conservative Space and Time Regularizations for the ICON Model (Artikel) 2009, ISSN: 1614-1199. @article{1, name = {Conservative Space and Time Regularizations for the ICON Model}, author = {M. Giorgetta, T. Hundertmark, P. Korn, S. Reich, and M. Restelli}, editor = {Reports on Earth System Science, 67 :1-32.}, issn = {1614-1199}, year = {2009}, date = {2009-01-01}, abstract = {In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows.}, } In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows. |

D. Hertwig I. Bastigkeit, Leitl; Schatzmann, Detecting coherent flow structures within and above a simplified urban roughness (Artikel) 2009. (BibTeX) @article{1, name = {Detecting coherent flow structures within and above a simplified urban roughness}, author = {D. Hertwig, I. Bastigkeit, B. Leitl, and M. Schatzmann}, editor = {Proceedings of PHYSMOD2009.}, year = {2009}, date = {2009-01-01}, } |

M. Dumbser G. Gassner,; Munz, Discontinuous Galerkin-Verfahren für zeitabhängige Advektions-Diffusions-Gleichungen (Artikel) 2009. (BibTeX) @article{1, name = {Discontinuous Galerkin-Verfahren für zeitabhängige Advektions-Diffusions-Gleichungen}, author = {M. Dumbser, G. Gassner, and C.-D. Munz}, editor = {Jahresbericht der DMV, 113(3):87-123.}, year = {2009}, date = {2009-01-01}, } |

Juan P Mellado Heiko Schmidt, Bjorn Stevens; Peters, Norbert DNS of the turbulent cloud-top mixing layer (Artikel) 2009. (BibTeX) @article{1, name = {DNS of the turbulent cloud-top mixing layer}, author = {Juan P Mellado, Heiko Schmidt, Bjorn Stevens, and Norbert Peters}, editor = {In: 12th EUROMECH European Turbulence Conference, Marburg, Germany.}, year = {2009}, date = {2009-01-01}, } |

U. Harlander R. Faulwetter, Alexandrov; Egbers, Estimating local instabilities from data with application to geophysical flows (Artikel) 2009, ISBN: 3-642-03084-X. (BibTeX) @article{1, name = {Estimating local instabilities from data with application to geophysical flows}, author = {U. Harlander, R. Faulwetter, K. Alexandrov, and C. Egbers}, editor = {In: Advances in Turbulence XII. Springer Proceedings in Physics 132, ed. by Eckhardt, B.. Springer, chap. ., pp. 163-167.}, note = {ISBN-10:3-642-03084-X EAN:9783642030840}, isbn = {3-642-03084-X}, year = {2009}, date = {2009-01-01}, note = {ISBN-10:3-642-03084-X EAN:9783642030840}, } |

Queck,; Bienert, Estimation of PBL model parameters from high resolution vegetation scans (Artikel) 2009. @article{1, name = {Estimation of PBL model parameters from high resolution vegetation scans}, author = {R. Queck and A. Bienert}, editor = {In: Geophysical Research Abstracts, vol. 11, EGU2009-10888.}, year = {2009}, date = {2009-01-01}, abstract = {The spatial patterns of turbulent fluxes over forests are dominated by inhomogeneities like step changes in stand height and forest clearings. A major limitation in the application of turbulence closure models to plant canopies is the parameterization of plant architecture. Terrestrial laser scanning is a fast developing tool and appears to be an efficient method to record 3D models of the vegetation. Using the measured wind profiles this study aims to validate and develop estimates of parameters like mixing length, displacement height and roughness length from the plant area density profile. Since May 2008 intensive measurements take place around a forest clearing („Wildacker“, Tharandter Wald, N 50°57’49", E 13°34’01") associated with this task. In total 25 measurement points, at 4 towers (heights: 40m, 40m, 40m, 30m) including five at ground level position (2 m), are used to record the turbulent flow at the same time. The forest stands around the clearing (500 m x 60 m) were scanned applying a terrestrial laser scanner. Thereby scans from different ground positions and from the top of the main tower (height: 40m) were done. The scans were filtered and combined to a single 3D representation of the stands. The detection of trees was done automatically and mean tree distances were calculated. The 3D point cloud of a selected tree group was transformed into a 3D voxel space. The normalised point density of each voxel represents the plant area density. Then, the spatial arrangement of points inside the voxel can be used to derive a parameterization for the drag coefficients. Simultaneously, the drag coefficients are calculated from turbulence measurements at the positions of anemometers. Finally the dependency can be investigated between drag coefficients, plant area density and plant area distribution with respect to stability and wind speed.}, } The spatial patterns of turbulent fluxes over forests are dominated by inhomogeneities like step changes in stand height and forest clearings. A major limitation in the application of turbulence closure models to plant canopies is the parameterization of plant architecture. Terrestrial laser scanning is a fast developing tool and appears to be an efficient method to record 3D models of the vegetation. Using the measured wind profiles this study aims to validate and develop estimates of parameters like mixing length, displacement height and roughness length from the plant area density profile. Since May 2008 intensive measurements take place around a forest clearing („Wildacker“, Tharandter Wald, N 50°57’49", E 13°34’01") associated with this task. In total 25 measurement points, at 4 towers (heights: 40m, 40m, 40m, 30m) including five at ground level position (2 m), are used to record the turbulent flow at the same time. The forest stands around the clearing (500 m x 60 m) were scanned applying a terrestrial laser scanner. Thereby scans from different ground positions and from the top of the main tower (height: 40m) were done. The scans were filtered and combined to a single 3D representation of the stands. The detection of trees was done automatically and mean tree distances were calculated. The 3D point cloud of a selected tree group was transformed into a 3D voxel space. The normalised point density of each voxel represents the plant area density. Then, the spatial arrangement of points inside the voxel can be used to derive a parameterization for the drag coefficients. Simultaneously, the drag coefficients are calculated from turbulence measurements at the positions of anemometers. Finally the dependency can be investigated between drag coefficients, plant area density and plant area distribution with respect to stability and wind speed. |

Schatzmann, Michael; Leitl, Bernd Evaluation of Numerical Flow and Dispersion Models for Applications in Industrial and Urban Areas (Artikel) 2009. (BibTeX) @article{1, name = {Evaluation of Numerical Flow and Dispersion Models for Applications in Industrial and Urban Areas}, author = {Michael Schatzmann and Bernd Leitl}, editor = {Chem. Eng. Technol., 32(2):241-246.}, year = {2009}, date = {2009-01-01}, } |

A. Swart L.R.M. Maas, Harlander; Manders, Experimental observation of strong mixing due to internal wave focusing over sloping terrain (Artikel) 2009. (BibTeX) @article{1, name = {Experimental observation of strong mixing due to internal wave focusing over sloping terrain}, author = {A. Swart, L.R.M. Maas, U. Harlander, and U. Manders}, editor = {Dynamics of Atmospheres and Oceans, 50(1):16-34.}, note = {10.1016/j.dynatmoce.2009.08.003}, year = {2009}, date = {2009-01-01}, note = {10.1016/j.dynatmoce.2009.08.003}, } |

Stefan Jebens Oswald Knoth,; Weiner, Rüdiger Explicit Two-Step Peer Methods for the Compressible Euler Equations (Artikel) 2009. @article{1, name = {Explicit Two-Step Peer Methods for the Compressible Euler Equations}, author = {Stefan Jebens, Oswald Knoth, and Rüdiger Weiner}, editor = {Monthly Weather Review, 137(7):2380-2392.}, year = {2009}, date = {2009-01-01}, abstract = {A new time-splitting method for the integration of the compressible Euler equations is presented. It is based on a two-step peer method which is a general linear method with second-order accuracy in every stage. The scheme uses a computationally very efficient forward-backward scheme for the integration of the high-frequency acoustic modes. With this splitting approach it is possible to integrate stably the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler equations and a comparison with the common split-explicit second-order three-stage Runge-Kutta method by Wicker and Skamarock shows the potential of the class of peer methods with respect to computational efficiency, stability and accuracy.}, } A new time-splitting method for the integration of the compressible Euler equations is presented. It is based on a two-step peer method which is a general linear method with second-order accuracy in every stage. The scheme uses a computationally very efficient forward-backward scheme for the integration of the high-frequency acoustic modes. With this splitting approach it is possible to integrate stably the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler equations and a comparison with the common split-explicit second-order three-stage Runge-Kutta method by Wicker and Skamarock shows the potential of the class of peer methods with respect to computational efficiency, stability and accuracy. |

A. Gerisch J. Lang, Podhaisky; Weiner, High-order linearly implicit two-step peer-finite element method for time-dependent PDEs (Artikel) 2009. (BibTeX) @article{1, name = {High-order linearly implicit two-step peer-finite element method for time-dependent PDEs}, author = {A. Gerisch, J. Lang, H. Podhaisky, and R. Weiner}, editor = {Applied Numerical Mathematics, 59:624-638.}, year = {2009}, date = {2009-01-01}, } |

A. Stenke M. Dameris, Grewe; Garny, Implications of Lagrangian transport for simulations with a coupled chemistry-climate model (Artikel) 2009. (BibTeX) @article{1, name = {Implications of Lagrangian transport for simulations with a coupled chemistry-climate model}, author = {A. Stenke, M. Dameris, V. Grewe, and H. Garny}, editor = {Atmospheric Chemistry and Physics , 9:5489-5504.}, year = {2009}, date = {2009-01-01}, } |

U. Harlander H. Ridderinkhof, Schouten; Ruijter, PM De Long term observations of transport, eddies, and Rossby waves in the Mozambique Channel (Artikel) 2009. @article{1, name = {Long term observations of transport, eddies, and Rossby waves in the Mozambique Channel}, author = {U. Harlander, H. Ridderinkhof, M. W Schouten, and W. PM De Ruijter}, editor = {J. Geophys. Res, 114(CO2003).}, year = {2009}, date = {2009-01-01}, abstract = {Data from an array of current meter moorings covering a period of two and a half years are used to estimate the varying transport through the Mozambique Channel. The total transport during this period is small (8.6 · 106 m3 s−1 or 8.6 Sv southward). Below 1200 m the transport is weak but a prominent deep western boundary undercurrent with cores at 1700 and 2200 m is found that transports 1.5 Sv to the north. The transport shows a large temporal variability, and neither a continuous upper layer western boundary current nor a continuous deep undercurrent is found. The variability in the upper layer is dominated by a period of 68 days and results mainly from eddies that migrate southward through the Mozambique Channel. In addition to this southward propagation, a westward-propagating signal is evident from a space-time diagram of the throughflow. The signal is interpreted as a Mozambique Channel Rossby normal mode. This interpretation is consistent with results from a Principal Oscillation Pattern Analysis (that estimates normal modes from the data) and a quasi-geostrophic channel model. A detailed inspection of a single “eddy event” shows that a precursor of an anticyclone is a strong southward current along the Madagascar coast that propagates westward to the center of the Channel. During the westward propagation, the current becomes unstable inducing an anticyclone. This scenario connects the westward-propagating mode with the eddy growth and explains the coincidence of the eddy and Rossby mode frequency. Still, the type of instability that leads to eddy growth could not be determined yet.}, } Data from an array of current meter moorings covering a period of two and a half years are used to estimate the varying transport through the Mozambique Channel. The total transport during this period is small (8.6 · 106 m3 s−1 or 8.6 Sv southward). Below 1200 m the transport is weak but a prominent deep western boundary undercurrent with cores at 1700 and 2200 m is found that transports 1.5 Sv to the north. The transport shows a large temporal variability, and neither a continuous upper layer western boundary current nor a continuous deep undercurrent is found. The variability in the upper layer is dominated by a period of 68 days and results mainly from eddies that migrate southward through the Mozambique Channel. In addition to this southward propagation, a westward-propagating signal is evident from a space-time diagram of the throughflow. The signal is interpreted as a Mozambique Channel Rossby normal mode. This interpretation is consistent with results from a Principal Oscillation Pattern Analysis (that estimates normal modes from the data) and a quasi-geostrophic channel model. A detailed inspection of a single “eddy event” shows that a precursor of an anticyclone is a strong southward current along the Madagascar coast that propagates westward to the center of the Channel. During the westward propagation, the current becomes unstable inducing an anticyclone. This scenario connects the westward-propagating mode with the eddy growth and explains the coincidence of the eddy and Rossby mode frequency. Still, the type of instability that leads to eddy growth could not be determined yet. |

Bordas,; Thevenin, Modeling cumulus clouds in a two-phase wind tunnel (Artikel) 2009. (BibTeX) @article{1, name = {Modeling cumulus clouds in a two-phase wind tunnel}, author = {R Bordas and D. Thevenin}, editor = {Miscellaneous publication.}, year = {2009}, date = {2009-01-01}, } |

R. Queck A. Bienert,; (2009), Harmansa Modeling wind fields in tall canopies - towards better momentum distribution using 3D vegetation scans in high resolution (Konferenz) 2009. (BibTeX) @conference{1, name = {Modeling wind fields in tall canopies - towards better momentum distribution using 3D vegetation scans in high resolution}, author = {R. Queck, A. Bienert, and S. Harmansa (2009)}, editor = {In: Konferenzbeitrag.}, note = {2nd International Conference “Wind Effects on Trees”. Albert-Ludwigs-University of Freiburg, Germany, 13-16 October 2009}, year = {2009}, date = {2009-01-01}, note = {2nd International Conference “Wind Effects on Trees”. Albert-Ludwigs-University of Freiburg, Germany, 13-16 October 2009}, } |

Daniel Ruprecht Rupert Klein,; Majda, Andrew MOISTURE-GRAVITY WAVE INTERACTIONS IN A MULTISCALE ENVIRONMENT (Artikel) 2009. @article{1, name = {MOISTURE-GRAVITY WAVE INTERACTIONS IN A MULTISCALE ENVIRONMENT}, author = {Daniel Ruprecht, Rupert Klein, and Andrew J Majda}, editor = {Preprint}, url = {http://opus.kobv.de/zib/volltexte/2009/1184/pdf/ZR_09_21.pdf}, year = {2009}, date = {2009-01-01}, abstract = {Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated.}, } Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated. |

von Larcher, Thomas; Klein, Rupert Multiple Scales in Fluid Dynamics and Meteorology - The DFG Priority Programme 1276 MetStröm (Artikel) 2009. (BibTeX) @article{1, name = {Multiple Scales in Fluid Dynamics and Meteorology - The DFG Priority Programme 1276 MetStröm}, author = {Thomas von Larcher and Rupert Klein}, editor = {Miscellaneous publication, Poster.}, note = {Poster presented at 'Scoping Meeting on Multi-scale Modelling of the Atmosphere and Ocean', Isaac Newton Institute for Mathematical Sciences, March 24th-26th, 2009, Reading, UK.}, year = {2009}, date = {2009-01-01}, note = {Poster presented at 'Scoping Meeting on Multi-scale Modelling of the Atmosphere and Ocean', Isaac Newton Institute for Mathematical Sciences, March 24th-26th, 2009, Reading, UK.}, } |

Jörg Wensch Oswald Knoth,; Galant, Alexander Multirate infinitesimal step methods for atmospheric flow simulation (Artikel) 2009. @article{1, name = {Multirate infinitesimal step methods for atmospheric flow simulation}, author = {Jörg Wensch, Oswald Knoth, and Alexander Galant}, editor = {BIT Numerical Mathematics, 49(2):449-473.}, url = {http://www.springerlink.com/content/25g707347w53p252?p=57e37f0100114de3a0334cb03bec902b&pi=5}, year = {2009}, date = {2009-01-01}, abstract = {he numerical solution of the Euler equations requires the treatment of processes in different temporal scales. Sound waves propagate fast compared to advective processes. Based on a spatial discretisation on staggered grids, a multirate time integration procedure is presented here generalising split-explicit Runge-Kutta methods. The advective terms are integrated by a Runge-Kutta method with a macro stepsize restricted by the CFL number. Sound wave terms are treated by small time steps respecting the CFL restriction dictated by the speed of sound. Split-explicit Runge-Kutta methods are generalised by the inclusion of fixed tendencies of previous stages. The stability barrier for the acoustics equation is relaxed by a factor of two. Asymptotic order conditions for the low Mach case are given. The relation to commutator-free exponential integrators is discussed. Stability is analysed for the linear acoustic equation. Numerical tests are executed for the linear acoustics and the nonlinear Euler equations.}, } he numerical solution of the Euler equations requires the treatment of processes in different temporal scales. Sound waves propagate fast compared to advective processes. Based on a spatial discretisation on staggered grids, a multirate time integration procedure is presented here generalising split-explicit Runge-Kutta methods. The advective terms are integrated by a Runge-Kutta method with a macro stepsize restricted by the CFL number. Sound wave terms are treated by small time steps respecting the CFL restriction dictated by the speed of sound. Split-explicit Runge-Kutta methods are generalised by the inclusion of fixed tendencies of previous stages. The stability barrier for the acoustics equation is relaxed by a factor of two. Asymptotic order conditions for the low Mach case are given. The relation to commutator-free exponential integrators is discussed. Stability is analysed for the linear acoustic equation. Numerical tests are executed for the linear acoustics and the nonlinear Euler equations. |

M. Schlegel O Knoth, Arnold; Wolke, Multirate Runge-Kutta schemes for advection equations (Artikel) 2009. (BibTeX) @article{1, name = {Multirate Runge-Kutta schemes for advection equations}, author = {M. Schlegel, O Knoth, M Arnold, and R. Wolke}, editor = {Journal of Computational and Applied Mathematics, 226(2):345-357.}, year = {2009}, date = {2009-01-01}, } |

Heiko Schmidt Juan P Mellado, Norbert Peters Alan Kerstein; Stevens, Bjorn Numerical study of buoyancy reversal in stably stratified flows (Artikel) 2009. @article{1, name = {Numerical study of buoyancy reversal in stably stratified flows}, author = {Heiko Schmidt, Juan P Mellado, Norbert Peters, Alan R Kerstein, and Bjorn Stevens}, editor = {In: European Geosciences Union General Assembly, Vienna.}, year = {2009}, date = {2009-01-01}, abstract = {Recent work suggests that shallow cumulus convection is the major point of departure among climate-model representations of climate sensitivity. A characteristic feature of the stratocumulus-topped boundary layer (STBL) is the contact discontinuity, and accompanying sharp temperature inversion, that separates the top of the cloud from the overlying quasi-laminar, free troposphere. This temperature inversion resists the tendency of the underlying turbulent layer to grow through entrainment into the free-troposphere, which allows the lower layer to moisten and clouds to develop therein. This sharp transition and the importance of the mixing between the two layers, greatly frustrates attempts to represent the STBL numerically, e.g. via large eddy simulation (LES), due to insufficient resolution. The subtile small scale interaction of molecular effects and turbulence might only be accessed using direct numerical simulation (DNS) and stochastic turbulence models where the latter keep full resolution of physical processes at least in one dimension. First we will present results of a stochastic one-dimensional mixing model used to explore laboratory analogs to the cloud top mixing problem. Here radiatively induced buoyancy reversal is investigated. Further we explore the buoyancy reversal problem using 2D and 3D DNS. The basic configuration now is a two-layer system, stably stratified because of the temperature difference between the two layers but undergoing evaporative cooling in the mixing regions, which may lead to buoyancy reversal.}, } Recent work suggests that shallow cumulus convection is the major point of departure among climate-model representations of climate sensitivity. A characteristic feature of the stratocumulus-topped boundary layer (STBL) is the contact discontinuity, and accompanying sharp temperature inversion, that separates the top of the cloud from the overlying quasi-laminar, free troposphere. This temperature inversion resists the tendency of the underlying turbulent layer to grow through entrainment into the free-troposphere, which allows the lower layer to moisten and clouds to develop therein. This sharp transition and the importance of the mixing between the two layers, greatly frustrates attempts to represent the STBL numerically, e.g. via large eddy simulation (LES), due to insufficient resolution. The subtile small scale interaction of molecular effects and turbulence might only be accessed using direct numerical simulation (DNS) and stochastic turbulence models where the latter keep full resolution of physical processes at least in one dimension. First we will present results of a stochastic one-dimensional mixing model used to explore laboratory analogs to the cloud top mixing problem. Here radiatively induced buoyancy reversal is investigated. Further we explore the buoyancy reversal problem using 2D and 3D DNS. The basic configuration now is a two-layer system, stably stratified because of the temperature difference between the two layers but undergoing evaporative cooling in the mixing regions, which may lead to buoyancy reversal. |

Horenko, On robust estimation of low-frequency variability trends in discrete Markovian sequences of atmospherical circulation patterns (Artikel) 2009. (BibTeX) @article{1, name = {On robust estimation of low-frequency variability trends in discrete Markovian sequences of atmospherical circulation patterns}, author = {I. Horenko}, editor = {Journal of Atmospheric Sciences, 66(7):2059-2072.}, year = {2009}, date = {2009-01-01}, } |

Horenko, On structure-preserving persistent clustering of multivariate time series (Artikel) 2009. (BibTeX) @article{1, name = {On structure-preserving persistent clustering of multivariate time series}, author = {I. Horenko}, editor = {Journal of Computational Physics.}, year = {2009}, date = {2009-01-01}, } |

Gregor J Gassner Frieder Lörcher, Claus-Dieter Munz; Hesthaven, Jan Polymorphic nodal elements and their application in discontinuous Galerkin methods (Artikel) 2009. @article{1, name = {Polymorphic nodal elements and their application in discontinuous Galerkin methods}, author = {Gregor J Gassner, Frieder Lörcher, Claus-Dieter Munz, and Jan S Hesthaven}, editor = {Journal of Computational Physics, 228(5):1573-1590.}, url = {Online version available http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHY-4V0TD95-1&_user=479010&_coverDate=03%2F20%2F2009&_alid=902934758&_rdoc=1&_fmt=high&_orig=search&_cdi=6863&_sort=d&_docanchor=&view=c&_ct=7&_acct=C000022964&_version=1&_urlVersion=0&_userid=479010&md5=6e31d9bf9d5989a30490a51369ee8abd}, year = {2009}, date = {2009-01-01}, } |

I. Bastigkeit D. Hertwig, Leitl; Schatzmann, Quality (and quantity) requirements for compiling LES-specific validation data sets from systematic wind tunnel modeling (Artikel) 2009. (BibTeX) @article{1, name = {Quality (and quantity) requirements for compiling LES-specific validation data sets from systematic wind tunnel modeling}, author = {I. Bastigkeit, D. Hertwig, B. Leitl, and M. Schatzmann}, editor = {Proceedings of PHYSMOD2009.}, year = {2009}, date = {2009-01-01}, } |

Schatzmann, Michael; Britter, Quality assurance and improvement of micro-scale meteorological models (Artikel) 2009. (BibTeX) @article{1, name = {Quality assurance and improvement of micro-scale meteorological models}, author = {Michael Schatzmann and R Britter}, editor = {Int. J. of Environment and Pollution.}, note = {(accepted)}, year = {2009}, date = {2009-01-01}, note = {(accepted)}, } |

S. Brdar A. Dedner, Klöfkorn Kränkel; Kröner, Simulation of Geophysical Problems with Dune-Fem (Artikel) 2009. (BibTeX) @article{1, name = {Simulation of Geophysical Problems with Dune-Fem}, author = {S. Brdar, A. Dedner, R. Klöfkorn, M. Kränkel, and D. Kröner}, editor = {In: ., vol. 115. Notes on Numerical Fluid Mechanics and Multidisciplinary Design.}, year = {2009}, date = {2009-01-01}, } |

M. Mei B. Leitl, Fischer; Schatzmann, Systematic analysis of puff dispersion in a semi-idealized urban roughness (Artikel) 2009. (BibTeX) @article{1, name = {Systematic analysis of puff dispersion in a semi-idealized urban roughness}, author = {M. Mei, B. Leitl, R. Fischer, and M. Schatzmann}, editor = {Proceedings of PHYSMOD2009.}, year = {2009}, date = {2009-01-01}, } |

Ch. Franzke I. Horenko, Majda; Klein, Systematic Metastable Atmospheric Regime Identification in an AGCM (Artikel) 2009. (BibTeX) @article{1, name = {Systematic Metastable Atmospheric Regime Identification in an AGCM}, author = {Ch. Franzke, I. Horenko, A. J Majda, and R. Klein}, editor = {Journal of Atmospheric Sciences, 66(7):1997-2012.}, year = {2009}, date = {2009-01-01}, } |

S. Löbig A. Dörnbrack, Fröhlich Hertel Ch. Kühnlein; Lang, Towards Large-Eddy Simulation on moving grids (Artikel) 2009. (BibTeX) @article{1, name = {Towards Large-Eddy Simulation on moving grids}, author = {S. Löbig, A. Dörnbrack, J. Fröhlich, C. Hertel, Ch. Kühnlein, and J. J. Lang}, editor = {PAMM:445-446.}, year = {2009}, date = {2009-01-01}, } |

Rupert Klein K.R. Bates,; Nikiforakis, Nikos Well Balanced Compressible Cut-Cell Simulation of Atmospheric Flow (Artikel) 2009. (BibTeX) @article{1, name = {Well Balanced Compressible Cut-Cell Simulation of Atmospheric Flow}, author = {Rupert Klein, K.R. Bates, and Nikos Nikiforakis}, editor = {Philosophical Transactions of the Royal Society.}, year = {2009}, date = {2009-01-01}, } |

## 2008 |

G. Gassner F. Lörcher,; Munz, A Discontinuous Galerkin Scheme based on a Space-time Expansion II. Viscous Flow Equations in Multi Dimensions (Artikel) 2008. (BibTeX) @article{1, name = {A Discontinuous Galerkin Scheme based on a Space-time Expansion II. Viscous Flow Equations in Multi Dimensions}, author = {G. Gassner, F. Lörcher, and C.-D. Munz}, editor = {Journal of Scientific Computing, 34(3):260-286.}, year = {2008}, date = {2008-01-01}, } |

P. Bastian M. Blatt, Dedner Engwer Klöfkorn Kornhuber Ohlberger; Sander, A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE (Artikel) 2008. @article{22, name = {A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE}, author = {P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander}, editor = {Computing, 82(2-3):121-138.}, year = {2008}, date = {2008-01-01}, abstract = {In a companion paper (Bastian et al. 2007, this issue) we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structures. Thus, user implementations become independent of the underlying grid implementation. Modern C++ template techniques are used to provide an interface implementation without big performance losses. The implementation is realized as part of the software environment DUNE (http://dune-project.org/). Numerical tests demonstrate the flexibility and the efficiency of our approach}, } In a companion paper (Bastian et al. 2007, this issue) we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structures. Thus, user implementations become independent of the underlying grid implementation. Modern C++ template techniques are used to provide an interface implementation without big performance losses. The implementation is realized as part of the software environment DUNE (http://dune-project.org/). Numerical tests demonstrate the flexibility and the efficiency of our approach |

Kühnlein, Adaptive meshes for meteorological applications (Artikel) 2008. (BibTeX) @article{1, name = {Adaptive meshes for meteorological applications}, author = {C. Kühnlein}, editor = {Miscellaneous publication, Posterpräsentation.}, note = {Sommerschule: Atmospheric Boundary Layers: Concepts, Observations, and Numerical Simulations in Les Houches, Frankreich}, year = {2008}, date = {2008-01-01}, note = {Sommerschule: Atmospheric Boundary Layers: Concepts, Observations, and Numerical Simulations in Les Houches, Frankreich}, } |

I. Horenko R. Klein, Dolaptchiev; Schütte, Ch. Automated Generation of Reduced Stochastic Weather Models I: simultaneous dimension and model reduction for time series analysis (Artikel) 2008. (BibTeX) @article{1, name = {Automated Generation of Reduced Stochastic Weather Models I: simultaneous dimension and model reduction for time series analysis}, author = {I. Horenko, R. Klein, S. Dolaptchiev, and Ch. Schütte}, editor = {SIAM Mult. Mod. Sim., 6(4):1125-1145.}, year = {2008}, date = {2008-01-01}, } |

T Hagemeier R Bordas, Bencs Wunderlich; (ed.), Thevenin Determination of Droplet Size and Velocity Distributions in a Two-Phase Wind Tunnel (Artikel) 2008. (BibTeX) @article{1, name = {Determination of Droplet Size and Velocity Distributions in a Two-Phase Wind Tunnel}, author = {T Hagemeier, R Bordas, P Bencs, B Wunderlich, and D Thevenin (ed.)}, editor = {vol. 13th International Symposium on Flow Visualization.}, note = {13th International Symposium on Flow Visualization, p. 094/1-094/10}, year = {2008}, date = {2008-01-01}, note = {13th International Symposium on Flow Visualization, p. 094/1-094/10}, } |

Craig,; Dörnbrack, Entrainment in Cumulus Clouds: What resolution is cloud resolving? (Artikel) 2008. (BibTeX) @article{1, name = {Entrainment in Cumulus Clouds: What resolution is cloud resolving?}, author = {C.G. Craig and A. Dörnbrack}, editor = {J. Atmos. Sci., 65:3978-3988.}, year = {2008}, date = {2008-01-01}, } |

Harlander,; Alexandrov, EULAG: a model system for multiple scale flows (Artikel) 2008. (BibTeX) @article{1, name = {EULAG: a model system for multiple scale flows}, author = {U. Harlander and K. Alexandrov}, editor = {In: EULAG mini-workshop, DLR Oberpfaffenhofen (Dr. Andreas Dörnbrack).}, note = {28. Juli - 30. Juli 2008}, year = {2008}, date = {2008-01-01}, note = {28. Juli - 30. Juli 2008}, } |

T. von Larcher J. Patz,; Harlander, Experiments on baroclinic instability in a differentially heated rotating annulus with inclined bottom (Artikel) 2008. (BibTeX) @article{1, name = {Experiments on baroclinic instability in a differentially heated rotating annulus with inclined bottom}, author = {T. von Larcher, J. Patz, and U. Harlander}, editor = {In: Geophysical Research Abstracts, EGU General Assembly, 10, EGU2008-A-03568.}, year = {2008}, date = {2008-01-01}, } |

John, Volker; Schmeyer, Ellen Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion (Artikel) 2008. (BibTeX) @article{1, name = {Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion}, author = {Volker John and Ellen Schmeyer}, editor = {Comput. Meth. Appl. Mech. Engrg.(198):475 - 494.}, year = {2008}, date = {2008-01-01}, } |

Markus Letzel M Krane,; Raasch, Sigfried High resolution urban large-eddy simulation studies from street canyon to neighbourhood scale (Artikel) 2008. (BibTeX) @article{1, name = {High resolution urban large-eddy simulation studies from street canyon to neighbourhood scale}, author = {Markus Letzel, M Krane, and Sigfried Raasch}, editor = {Atmospheric Environment, 42(38):8770-8784.}, year = {2008}, date = {2008-01-01}, } |

Teleaga,; Lang, Higher-order linearly implicit one-step methods for three-dimensional incompressible Navier-Strokes equations (Artikel) 2008. (BibTeX) @article{1, name = {Higher-order linearly implicit one-step methods for three-dimensional incompressible Navier-Strokes equations}, author = {I. Teleaga and J. Lang}, editor = {Studia Babes-Bolyai Matematica, 53:109-121.}, year = {2008}, date = {2008-01-01}, } |

S. Tomm D.A. von Terzi,; Fröhlich, Interaction of the filter and spatial discretisation operators for Large-Eddy Simulation using the Approximate Deconvolution Model (Artikel) 2008. (BibTeX) @article{1, name = {Interaction of the filter and spatial discretisation operators for Large-Eddy Simulation using the Approximate Deconvolution Model}, author = {S. Tomm, D.A. von Terzi, and J. Fröhlich}, editor = {PAMM, 8:10605-10606.}, year = {2008}, date = {2008-01-01}, } |

Illia Horenko Stamen Dolaptchiev, Eliseev Mokhov; Klein, Rupert Metastable decomposition of high-dimensional meteorological data with gaps (Artikel) 2008. (BibTeX) @article{1, name = {Metastable decomposition of high-dimensional meteorological data with gaps}, author = {Illia Horenko, Stamen Dolaptchiev, A Eliseev, I Mokhov, and Rupert Klein}, editor = {Journal of the Atmospheric Sciences, 65:3479-3496.}, year = {2008}, date = {2008-01-01}, } |

Pincus, Robert; Stevens, Bjorn Monte Carlo spectral integration: A consistent approximation for radiative transfer in large eddy simulations (Artikel) 2008. @article{1, name = {Monte Carlo spectral integration: A consistent approximation for radiative transfer in large eddy simulations}, author = {Robert Pincus and Bjorn Stevens}, editor = {Journal of Advances in Modeling Earth Systems.}, url = {http://adv-model-earth-syst.org/index.php/JAMES/article/view/4}, year = {2008}, date = {2008-01-01}, abstract = {Large-eddy simulation (LES) refers to a class of calculations in which the large energy-rich eddies are simulated directly and are insensitive to errors in the modeling of sub-grid scale processes. Flows represented by LES are often driven by radiative heating and therefore require the calculation of radiative transfer along with the fluid-dynamical simulation. Current methods for detailed radiation calculations, even those using simple one-dimensional radiative transfer, are far too expensive for routine use, while popular shortcuts are either of limited applicability or run the risk of introducing errors on time and space scales that might affect the overall simulation. A new approximate method is described that relies on Monte Carlo sampling of the spectral integration in the heating rate calculation and is applicable to any problem. The error introduced when using this method is substantial for individual samples (single columns at single times) but is uncorrelated in time and space and so does not bias the statistics of scales that are well resolved by the LES. The method is evaluated through simulation of two test problems; these behave as expected. A scaling analysis shows that the errors introduced by the method diminish as flow features become well resolved. Errors introduced by the approximation increase with decreasing spatial scale but the spurious energy introduced by the approximation is less than the energy expected in the unperturbed flow, i.e. the energy associated with the spectral cascade from the large scale, even on the grid scale.}, } Large-eddy simulation (LES) refers to a class of calculations in which the large energy-rich eddies are simulated directly and are insensitive to errors in the modeling of sub-grid scale processes. Flows represented by LES are often driven by radiative heating and therefore require the calculation of radiative transfer along with the fluid-dynamical simulation. Current methods for detailed radiation calculations, even those using simple one-dimensional radiative transfer, are far too expensive for routine use, while popular shortcuts are either of limited applicability or run the risk of introducing errors on time and space scales that might affect the overall simulation. A new approximate method is described that relies on Monte Carlo sampling of the spectral integration in the heating rate calculation and is applicable to any problem. The error introduced when using this method is substantial for individual samples (single columns at single times) but is uncorrelated in time and space and so does not bias the statistics of scales that are well resolved by the LES. The method is evaluated through simulation of two test problems; these behave as expected. A scaling analysis shows that the errors introduced by the method diminish as flow features become well resolved. Errors introduced by the approximation increase with decreasing spatial scale but the spurious energy introduced by the approximation is less than the energy expected in the unperturbed flow, i.e. the energy associated with the spectral cascade from the large scale, even on the grid scale. |

von Larcher, Thomas; Klein, Rupert Multiscale Problems in Fluid Dynamics and Meteorology: the DFG priority programme MetStröm (Artikel) 2008. (BibTeX) @article{1, name = {Multiscale Problems in Fluid Dynamics and Meteorology: the DFG priority programme MetStröm}, author = {Thomas von Larcher and Rupert Klein}, editor = {Miscellaneous publication, EGU 2008, Poster.}, year = {2008}, date = {2008-01-01}, } |

J.D. Doyle V. Grubišić, Brown De Wekker Dörnbrack Jiang Mayor; Weissmann, Observations and Numerical Simulations of Subrotor Vortices during T-REX (Artikel) 2008. (BibTeX) @article{1, name = {Observations and Numerical Simulations of Subrotor Vortices during T-REX}, author = {J.D. Doyle, V. Grubišić, W.O.J. Brown, S.F.J. De Wekker, A. Dörnbrack, Q. Jiang, S.D. Mayor, and M. Weissmann}, editor = {J. Atmos. Sci.}, year = {2008}, date = {2008-01-01}, } |

John, Volker; Schmeyer, Ellen On finite element methods for 3D time-dependent convection-diffusion-reaction equations with small diffusion (Artikel) 2008. (BibTeX) @article{1, name = {On finite element methods for 3D time-dependent convection-diffusion-reaction equations with small diffusion}, author = {Volker John and Ellen Schmeyer}, editor = {In: Proceedings of BAIL 2008.}, note = {Limerick, accepted for publication}, year = {2008}, date = {2008-01-01}, note = {Limerick, accepted for publication}, } |

Horenko, On Simultaneous Data-Based Dimension Reduction and Hidden Phase Identification (Artikel) 2008. @article{1, name = {On Simultaneous Data-Based Dimension Reduction and Hidden Phase Identification}, author = {I. Horenko}, editor = {Journal of Atmospheric Sciences, 65(6):1941-1954.}, year = {2008}, date = {2008-01-01}, abstract = {We consider a problem of simultaneous dimension reduction and identification of hidden attractive manifolds in multidimensional data with noise. The problem is approached in two consecutive steps: (i) embedding of the original data in a sufficiently high-dimensional extended space in a way proposed by F. Takens in his embedding theorem (F. Takens, in: Dynamical Systems and Turbulence, D.A. Rand and L.S. Young eds., Springer, New York, 1981) followed by (ii) a minimization of the residual–functional. We construct the residual– functional to measure the distance between the original data in extended space and their reconstruction based on a low dimensional description. The reduced representation of the analyzed data results from projection onto a fixed number of unknown low–dimensional manifolds. Two specific forms of the residual-functional are proposed. They define two different types of essential coordinates: (i) localized essential orthogonal functions (EOFs) and (ii) localized functions which we call principal original components(POC). The application of the framework is exemplified on a Lorenz–attractor model with measurement noise and on historical air temperature data. It is demonstrated how the new method can be used for the elimination of noise and identification of the seasonal lowfrequency components in meteorological data. We also present an application of the proposed POC-components in the context of the construction of low-dimensional predictive models.}, } We consider a problem of simultaneous dimension reduction and identification of hidden attractive manifolds in multidimensional data with noise. The problem is approached in two consecutive steps: (i) embedding of the original data in a sufficiently high-dimensional extended space in a way proposed by F. Takens in his embedding theorem (F. Takens, in: Dynamical Systems and Turbulence, D.A. Rand and L.S. Young eds., Springer, New York, 1981) followed by (ii) a minimization of the residual–functional. We construct the residual– functional to measure the distance between the original data in extended space and their reconstruction based on a low dimensional description. The reduced representation of the analyzed data results from projection onto a fixed number of unknown low–dimensional manifolds. Two specific forms of the residual-functional are proposed. They define two different types of essential coordinates: (i) localized essential orthogonal functions (EOFs) and (ii) localized functions which we call principal original components(POC). The application of the framework is exemplified on a Lorenz–attractor model with measurement noise and on historical air temperature data. It is demonstrated how the new method can be used for the elimination of noise and identification of the seasonal lowfrequency components in meteorological data. We also present an application of the proposed POC-components in the context of the construction of low-dimensional predictive models. |

Schatzmann, Michael; Leitl, Bernd Properties of field and wind tunnel boundary layers within and above the urban canopy (Artikel) 2008, ISBN: 13 978-2-930389-85-0. (BibTeX) @article{1, name = {Properties of field and wind tunnel boundary layers within and above the urban canopy}, author = {Michael Schatzmann and Bernd Leitl}, editor = {In: Atmospheric boundary layer flows in air pollution modelling, ed. by van Beeck, J. P. A. J., Buchlin, J.-M., and Petrosyan, A.. VKI , chap. N.N., pp. N.N..}, isbn = {13 978-2-930389-85-0}, year = {2008}, date = {2008-01-01}, } |

Kühnlein,; Dörnbrack, Scalar advection with adaptive moving meshes (Artikel) 2008. (BibTeX) @article{1, name = {Scalar advection with adaptive moving meshes}, author = {C. Kühnlein and A. Dörnbrack}, editor = {In: 1st International Workshop of EULAG Users.}, note = {Bad Tölz zum Download auf der Webseite http://www.mmm.ucar.edu/eulag/WORKSHOP08/abstracts_volume_08.pdf}, year = {2008}, date = {2008-01-01}, note = {Bad Tölz zum Download auf der Webseite http://www.mmm.ucar.edu/eulag/WORKSHOP08/abstracts_volume_08.pdf}, } |

Baldauf, Stability analysis for linear discretisations of the advection equation (Artikel) Journal of Computational Physics, 227(13), 2008. @article{22, name = {Stability analysis for linear discretisations of the advection equation}, author = {M. Baldauf}, editor = {Journal of Computational Physics, 227(13):6638-6659.}, year = {2008}, date = {2008-01-01}, journal = {Journal of Computational Physics}, volume = {227(13)}, abstract = {For the 1-dim. linear advection problem stability limits of Runge–Kutta (RK) methods from 1st to 7th order in combination with upwind or centered difference schemes from 1st to 6th order are presented. The analysis can be carried out in a rather general way by introduction of a broad class of Runge–Kutta methods, here called ‘Linear Case Runge–Kutta (LC-RK)’ methods, which behave completely similar for linear, time-independent and homogeneous ODE-systems and contain the ‘classical’ order = stage RK methods. The set of conditions for the coefficients of these LC-RK-schemes could be derived explicitly for arbitrary order N. From an efficiency viewpoint the LC-RK 3rd order methods in combination with upwind 3rd or 5th order or the LC-RK 4th order scheme with 4th order centered difference advection are a good choice. The analysis can be extended easily to multidimensional splited advection for which a necessary stability condition is presented.}, } For the 1-dim. linear advection problem stability limits of Runge–Kutta (RK) methods from 1st to 7th order in combination with upwind or centered difference schemes from 1st to 6th order are presented. The analysis can be carried out in a rather general way by introduction of a broad class of Runge–Kutta methods, here called ‘Linear Case Runge–Kutta (LC-RK)’ methods, which behave completely similar for linear, time-independent and homogeneous ODE-systems and contain the ‘classical’ order = stage RK methods. The set of conditions for the coefficients of these LC-RK-schemes could be derived explicitly for arbitrary order N. From an efficiency viewpoint the LC-RK 3rd order methods in combination with upwind 3rd or 5th order or the LC-RK 4th order scheme with 4th order centered difference advection are a good choice. The analysis can be extended easily to multidimensional splited advection for which a necessary stability condition is presented. |

Vater, Stefan; Klein, Rupert Stability of a Projection Method for the Zero Froude Number Shallow Water Equations (Artikel) 2008. (BibTeX) @article{1, name = {Stability of a Projection Method for the Zero Froude Number Shallow Water Equations}, author = {Stefan Vater and Rupert Klein}, editor = {Numerische Mathematik.}, note = {accepted}, year = {2008}, date = {2008-01-01}, note = {accepted}, } |

Heiko Schmidt Juan P Mellado, Norbert Peters; Stevens, Bjorn Towards a modular superparameterization for Stratocumulus clouds considering unsteady entrainment (Artikel) 2008. @article{1, name = {Towards a modular superparameterization for Stratocumulus clouds considering unsteady entrainment}, author = {Heiko Schmidt, Juan P Mellado, Norbert Peters, and Bjorn Stevens}, editor = {Miscellaneous publication, 4th PAN-GCSS Meeting on "Advances in Modeling and Observing Clouds and Convection", Toulouse, France.}, year = {2008}, date = {2008-01-01}, abstract = {Low clouds are increasingly recognized as the main source of divergence in model based estimates of climate change. The best tool for understanding clouds and microphysical interactions is Large Eddy Simulation (LES), but fundamental issues emerge in precisely those quantities of interest (e.g. Albedo). A reason for this is that current LES cannot resolve the cloud interface physics due to insufficient grid resolution. Elaborate physically based subgrid models are numerically smeared out, so that a distinction between numerical and physical effects is impossible. Here, we propose a heterogeneous multi scale concept for the modeling of Stratocumulus clouds. The cloud top interface which is driven by large scale motions is explicitly followed (tracked) using a level set ansatz. At the same time the important small scale mixing process is considered by embedding (super-) parameterizations in a modular fashion. Therefore the entrainment process is investigated with different numerical and physical models, one is the classical Direct Numerical Simulations (DNS) approach, the second alternative is a stochastic concept based on a one dimensional turbulence model (ODT). First results concern entrainment in a stratified moist shear layer, cloud top layer stability and buoyancy reversal studies. The new approach has two key advantages. Firstly, using an interface method avoids numerical smearing. Secondly, the modular coupling procedure, which has been developed for combustion and two phase flow problems, helps to combine small scale entrainment physics with the large scales in a consistent manner.}, } Low clouds are increasingly recognized as the main source of divergence in model based estimates of climate change. The best tool for understanding clouds and microphysical interactions is Large Eddy Simulation (LES), but fundamental issues emerge in precisely those quantities of interest (e.g. Albedo). A reason for this is that current LES cannot resolve the cloud interface physics due to insufficient grid resolution. Elaborate physically based subgrid models are numerically smeared out, so that a distinction between numerical and physical effects is impossible. Here, we propose a heterogeneous multi scale concept for the modeling of Stratocumulus clouds. The cloud top interface which is driven by large scale motions is explicitly followed (tracked) using a level set ansatz. At the same time the important small scale mixing process is considered by embedding (super-) parameterizations in a modular fashion. Therefore the entrainment process is investigated with different numerical and physical models, one is the classical Direct Numerical Simulations (DNS) approach, the second alternative is a stochastic concept based on a one dimensional turbulence model (ODT). First results concern entrainment in a stratified moist shear layer, cloud top layer stability and buoyancy reversal studies. The new approach has two key advantages. Firstly, using an interface method avoids numerical smearing. Secondly, the modular coupling procedure, which has been developed for combustion and two phase flow problems, helps to combine small scale entrainment physics with the large scales in a consistent manner. |

Heiko Schmidt Juan P Mellado, Norbert Peters; Stevens, Bjorn Towards modular front tracking for Stratocumulus clouds considering unsteady entrainment processes (Artikel) 2008. @article{1, name = {Towards modular front tracking for Stratocumulus clouds considering unsteady entrainment processes}, author = {Heiko Schmidt, Juan P Mellado, Norbert Peters, and Bjorn Stevens}, editor = {Miscellaneous publication, European Geosciences Union General Assembly, Vienna, Austria .}, year = {2008}, date = {2008-01-01}, abstract = {Low clouds are increasingly recognized as the main source of divergence in model based estimates of climate change. Our best tool for understanding clouds and micro-physical interactions is Large Eddy Simulation (LES), but fundamental issues emerge in precisely those quantities of interest (e.g. Albedo). A reason for this is that current LES cannot resolve the cloud interface physics due to insufficient resolution. Elaborate physically based subgrid models are numerically smeared out (fed wrong), so that a distinction between numerical and physical effects is impossible. Here, we propose a heterogeneous multi scale concept for the modeling of Stratocumulus clouds. The cloud top interface which is driven by large scale motions is explicitly tracked using a level set method. At the same time the important small scale mixing process is considered by embedding (super-) parameterizations in a modular fashion. Therefore the entrainment process is investigated with Direct Numerical Simulations (DNS). The new approach has two key advantages. Firstly, using an interface method avoids numerical smearing. Secondly, the modular coupling procedure, which has been developed for combustion and two phase flow problems, helps to combine small scale entrainment physics with the large scales in a consistent manner.}, } Low clouds are increasingly recognized as the main source of divergence in model based estimates of climate change. Our best tool for understanding clouds and micro-physical interactions is Large Eddy Simulation (LES), but fundamental issues emerge in precisely those quantities of interest (e.g. Albedo). A reason for this is that current LES cannot resolve the cloud interface physics due to insufficient resolution. Elaborate physically based subgrid models are numerically smeared out (fed wrong), so that a distinction between numerical and physical effects is impossible. Here, we propose a heterogeneous multi scale concept for the modeling of Stratocumulus clouds. The cloud top interface which is driven by large scale motions is explicitly tracked using a level set method. At the same time the important small scale mixing process is considered by embedding (super-) parameterizations in a modular fashion. Therefore the entrainment process is investigated with Direct Numerical Simulations (DNS). The new approach has two key advantages. Firstly, using an interface method avoids numerical smearing. Secondly, the modular coupling procedure, which has been developed for combustion and two phase flow problems, helps to combine small scale entrainment physics with the large scales in a consistent manner. |

## 2007 |

F. Lörcher G. Gassner,; Munz, A Discontinuous Galerkin Scheme based on a Space-time Expansion I. Inviscid Compressible Flow in One Space Dimension (Artikel) 2007. (BibTeX) @article{1, name = {A Discontinuous Galerkin Scheme based on a Space-time Expansion I. Inviscid Compressible Flow in One Space Dimension}, author = {F. Lörcher, G. Gassner, and C.-D. Munz}, editor = {Journal of Scientific Computing, 32(2):175-199.}, year = {2007}, date = {2007-01-01}, } |

P. Bastian M. Blatt, Dedner Engwer Klöfkorn Ohlberger; Sander, A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework (Artikel) 2007. @article{22, name = {A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework}, author = {P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander}, editor = {Computing, 82(2-3):103-119.}, year = {2007}, date = {2007-01-01}, abstract = {We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches [2, 3], our grids have a hierarchical structure. This makes them suitable for geometric multigrid algorithms and hierarchical local grid refinement. The description is also general enough to include geometrically nonconforming grids. The definitions in this article serve as the basis for an implementation of an abstract grid interface as C++ classes in the DUNE framework [1].}, } We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches [2, 3], our grids have a hierarchical structure. This makes them suitable for geometric multigrid algorithms and hierarchical local grid refinement. The description is also general enough to include geometrically nonconforming grids. The definitions in this article serve as the basis for an implementation of an abstract grid interface as C++ classes in the DUNE framework [1]. |

Tomm, Fehlererfassung für die Large Eddy Simulation auf gestreckten Gittern (Artikel) 2007. (BibTeX) @article{1, name = {Fehlererfassung für die Large Eddy Simulation auf gestreckten Gittern}, author = {S. Tomm}, editor = {Master thesis, Diplomarbeit, Universität Karlsruhe, Institut für Hydromechanik.}, year = {2007}, date = {2007-01-01}, } |

Lang,; Verwer, On Global Error Estimation and Control for Initial Value Problems (Artikel) 2007. (BibTeX) @article{1, name = {On Global Error Estimation and Control for Initial Value Problems}, author = {J. Lang and J. Verwer}, editor = {SIAM J. Sci. Comp., 29:1460-1475.}, year = {2007}, date = {2007-01-01}, } |

Debrabant,; Lang, On Global Error Estimation and Control for Parabolic Equations (Artikel) 2007. (BibTeX) @article{1, name = {On Global Error Estimation and Control for Parabolic Equations}, author = {K. Debrabant and J. Lang}, editor = {Appl. Num. Math, submitted.}, year = {2007}, date = {2007-01-01}, } |

U. Harlander T. von Larcher,; Egbers, Referenzexperiment für Untersuchungen der Dynamik und Koexistenz von grossräumigen und kleinskaligen Strömungsstrukturen am Beispiel barokliner und Schwerewellen (Artikel) 2007. (BibTeX) @article{1, name = {Referenzexperiment für Untersuchungen der Dynamik und Koexistenz von grossräumigen und kleinskaligen Strömungsstrukturen am Beispiel barokliner und Schwerewellen}, author = {U. Harlander, T. von Larcher, and C. Egbers}, editor = {In: MetStroem Kick-off Treffen, FU Berlin, 1.-2. November 2007.}, year = {2007}, date = {2007-01-01}, } |

## 2006 |

Vater,; Klein, Stability of a Projection Method for the Zero Froude Number Shallow Water Equations (Artikel) 2006. (BibTeX) @article{1, name = {Stability of a Projection Method for the Zero Froude Number Shallow Water Equations}, author = {S. Vater and R. Klein}, editor = {Miscellaneous publication.}, note = {Eleventh International Conference on Hyperbolic Problems Theory, Numerics, Applications, July 17-21, 2006, École Normale Supérieure de Lyon, France.}, year = {2006}, date = {2006-01-01}, note = {Eleventh International Conference on Hyperbolic Problems Theory, Numerics, Applications, July 17-21, 2006, École Normale Supérieure de Lyon, France.}, } |

## 0000 |

von Harlander U., Larcher Th. Wright Hoff Alexandrov; Egbers, Orthogonal decomposition methods to analyze PIV, LDA and thermography data of a thermally driven rotating annulus laboratory experiment (Artikel) AGU Book Modelling Atmospheric and Oceanic flows: insights from laboratory experiments and numerical simulations, 0000. (BibTeX) @article{Harlander2014, name = { Orthogonal decomposition methods to analyze PIV, LDA and thermography data of a thermally driven rotating annulus laboratory experiment}, author = {Harlander, U., von Larcher, Th., Wright, G.B., Hoff, M., Alexandrov, K. and Egbers, C.}, editor = {von Larcher, Th. and Williams, P.}, note = {accepted for publishing, to appear in 2014 }, year = {0000}, date = {0000-00-00}, journal = {AGU Book Modelling Atmospheric and Oceanic flows: insights from laboratory experiments and numerical simulations}, note = {accepted for publishing, to appear in 2014 }, } |

Benacchio T., O'Neill Klein A blended soundproof-to-compressible numerical model for atmospheric dynamics (Artikel) Monthly Weather Review, 0000. @article{Benacchio2013, name = {A blended soundproof-to-compressible numerical model for atmospheric dynamics}, author = {Benacchio, T., O'Neill, W.P., Klein, R.}, note = {submitted}, year = {0000}, date = {0000-00-00}, journal = {Monthly Weather Review}, abstract = {A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo-incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown.}, note = {submitted}, } A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo-incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown. |

Siewert C., Kunnen Meinke Schröder Numerical Investigation of the Combined Effects of Gravity and Turbulence on the Motion of Small and Heavy Particles (Artikel) New Results in Numerical and Experimental Fluid Mechanics IX, Notes on Numerical Fluid Mechanics and M, 0000. (BibTeX) @article{Dillmann2013, name = {Numerical Investigation of the Combined Effects of Gravity and Turbulence on the Motion of Small and Heavy Particles}, author = {Siewert, C., Kunnen, R. P. J., Meinke, M. Schröder, W.}, editor = {Dillmann, A., Heller, G., Kreplin, H.-P., Nitsche, W., Peltzer, I.}, note = {to appear}, year = {0000}, date = {0000-00-00}, journal = {New Results in Numerical and Experimental Fluid Mechanics IX}, volume = {Notes on Numerical Fluid Mechanics and M}, series = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design}, note = {to appear}, } |

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#### int. Conference 2011