@inproceedings{SeeligHarlanderBorciaetal., author = {Seelig, Torsten and Harlander, Uwe and Borcia, Ion-Dan and Scurtu, Nicoleta and Egbers, Christoph and Klein, Marten and Ghasemi, Abouzar and Will, Andreas and Schaller, Eberhard}, title = {Inertial waves in rotating cylindrical annulus: theory, experiment and simulations}, series = {Book of abstracts, 9th European Fluid Mechanics Conference (EFMC), 9-13 September, Rome, Italy}, booktitle = {Book of abstracts, 9th European Fluid Mechanics Conference (EFMC), 9-13 September, Rome, Italy}, language = {en} } @inproceedings{SeeligBorciaKleinetal., author = {Seelig, Torsten and Borcia, Ion-Dan and Klein, Marten and Ghasemi, Abouzar and Will, Andreas and Egbers, Christoph and Schaller, Eberhard and Harlander, Uwe}, title = {Inertial waves and wave attractors in a rotating annulus with inner or outer cylinder libration}, series = {European Geosciences Union (EGU), 10th General Assembly, Vienna, Austria, 07 - 12 April 2013}, booktitle = {European Geosciences Union (EGU), 10th General Assembly, Vienna, Austria, 07 - 12 April 2013}, language = {en} } @misc{KleinSeeligKurganskyetal., author = {Klein, Marten and Seelig, Torsten and Kurgansky, Michael V. and Ghasemi, Abouzar and Borcia, Ion-Dan and Will, Andreas and Schaller, Eberhard and Egbers, Christoph and Harlander, Uwe}, title = {Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder}, series = {Journal of Fluid Mechanics}, journal = {Journal of Fluid Mechanics}, number = {vol. 751}, issn = {1750-6859}, doi = {10.1017/jfm.2014.304}, pages = {255 -- 297}, abstract = {The mechanism of localized inertial wave excitation and its efficiency is investigated for an annular cavity rotating with Ω0 . Meridional symmetry is broken by replacing the inner cylinder with a truncated cone (frustum). Waves are excited by individual longitudinal libration of the walls. The geometry is non-separable and exhibits wave focusing and wave attractors. We investigated laboratory and numerical results for the Ekman number E ≈ 10-6. inclination α = 5.71◦ and libration amplitudes ε 0.2 within the inertial wave band 0 < ω < 2Ω0 . Under the assumption that the inertial waves do not essentially affect the boundary-layer structure, we use classical boundary-layer analysis to study oscillating Ekman layers over a librating wall that is at an angle α = 0 to the axis of rotation. The Ekman layer erupts at frequency ω = f∗, where f∗ ≡ 2Ω0 sin α is the effective Coriolis parameter in a plane tangential to the wall. For the selected inclination this eruption occurs for the forcing frequency ω/Ω0 = 0.2. For the librating lids eruption occurs at ω/Ω0 = 2. The study reveals that the frequency dependence of the total kinetic energy Kω of the excited wave field is strongly connected to the square of the Ekman pumping velocity wE (ω) that, in the linear limit, becomes singular when the boundary layer erupts. This explains the frequency dependence of non-resonantly excited waves. By the localization of the forcing, the two configurations investigated, (i) frustum libration and (ii) lids together with outer cylinder in libration, can be clearly distinguished by their response spectra. Good agreement was found for the spatial structure of low-order wave attractors and periodic orbits (both characterized by a small number of reflections) in the frequency windows predicted by geometric ray tracing. For 'resonant' frequencies a significantly increased total bulk energy was found, while the energy in the boundary layer remained nearly constant. Inertial wave energy enters the bulk flow via corner beams, which are parallel to the characteristics of the underlying Poincar{\´e} problem. Numerical simulations revealed a mismatch between the wall-parallel mass fluxes near the corners. This leads to boundary-layer eruption and the generation of inertial waves in the corners.}, language = {en} } @inproceedings{KleinGhasemiSeeligetal., author = {Klein, Marten and Ghasemi, Abouzar and Seelig, Torsten and Borcia, Ion-Dan and Harlander, Uwe and Will, Andreas}, title = {DNS of inertial wave attractors in a librating annulus with height-dependent gap width}, series = {15th European turbulence conference (ETC), Delft, The Netherlands (2015)}, booktitle = {15th European turbulence conference (ETC), Delft, The Netherlands (2015)}, abstract = {Direct numerical simulations (DNS) of inertial wave attractors have been carried out in a librating Taylor-Couette system with broken mirror symmetry in the radial-axial cross-section. The inertial wave excitation mechanism and its localisation at the edges was clarified by applying boundary layer theory. Additional resonance peaks in the simulated response spectra were found to agree with low-order wave attractors obtained by geometric ray tracing. Numerics and theory are in qualitative agreement with recent lab experiments.}, language = {en} } @inproceedings{SeeligGhasemiKurganskyetal., author = {Seelig, Torsten and Ghasemi, Abouzar and Kurgansky, Michael V. and Klein, Marten and Will, Andreas and Harlander, Uwe}, title = {Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus}, series = {15th European turbulence conference (ETC), Delft, The Netherlands (2015)}, booktitle = {15th European turbulence conference (ETC), Delft, The Netherlands (2015)}, language = {en} } @inproceedings{KleinGhasemiSeeligetal., author = {Klein, Marten and Ghasemi, Abouzar and Seelig, Torsten and Borcia, Ion-Dan and Harlander, Uwe and Will, Andreas}, title = {Mean flow generation and inertial wave attractors in a librating annulus: DNS and theory}, series = {European Geosciences Union, General Assembly 2015, Vienna, Austria, 13 April - 17 May 2015}, booktitle = {European Geosciences Union, General Assembly 2015, Vienna, Austria, 13 April - 17 May 2015}, publisher = {European Geophysical Society}, address = {Katlenburg-Lindau}, language = {en} } @inproceedings{KleinGhasemiSeeligetal., author = {Klein, Marten and Ghasemi, Abouzar and Seelig, Torsten and Borcia, Ion-Dan and Harlander, Uwe and Will, Andreas}, title = {DNS of inertial wave attractors in a librating annular cavity with a height-dependent gap}, series = {ICTW 19, Book of Abstracts, 19th International Couette-Taylor Workshop, June 24 - 26, 2015 Cottbus, Germany}, booktitle = {ICTW 19, Book of Abstracts, 19th International Couette-Taylor Workshop, June 24 - 26, 2015 Cottbus, Germany}, address = {Cottbus}, pages = {122 -- 123}, language = {en} } @inproceedings{KleinBorciaEgbersetal., author = {Klein, Marten and Borcia, Ion-Dan and Egbers, Christoph and Ghasemi, Abouzar and Harlander, Uwe and Kurgansky, Michael V. and Schaller, Eberhard and Seelig, Torsten and Will, Andreas}, title = {Inertial Waves and Wave Excitation Mechanisms in Annular Cavities: Simulations, Experiments and Theory}, series = {European Turbulence Conference ETC14, Lyon, 2013}, booktitle = {European Turbulence Conference ETC14, Lyon, 2013}, pages = {2}, language = {en} } @inproceedings{KleinGhasemiHarlanderetal., author = {Klein, Marten and Ghasemi, Abouzar and Harlander, Uwe and Will, Andreas}, title = {Inertial wave excitation and wave attractors in a librating annulus: DNS}, series = {European Geosciences Union, General Assembly 2014, Vienna, Austria, 27 April - 02 May 2014}, booktitle = {European Geosciences Union, General Assembly 2014, Vienna, Austria, 27 April - 02 May 2014}, publisher = {European Geophysical Society}, address = {Katlenburg-Lindau}, language = {en} } @misc{GhasemiKleinHarlanderetal., author = {Ghasemi, Abouzar and Klein, Marten and Harlander, Uwe and Kurgansky, Michael V. and Schaller, Eberhard and Will, Andreas}, title = {Mean flow generation by G{\"o}rtler vortices in a rotating annulus with librating side walls}, series = {Physics of Fluids}, volume = {28}, journal = {Physics of Fluids}, number = {056603}, doi = {10.1063/1.4948406}, pages = {1 -- 23}, abstract = {Time periodic variation of the rotation rate of an annulus induces in supercritical regime an unstable Stokes boundary layer over the cylinder side walls, generating G{\"o}rtler vortices in a portion of a libration cycle as a discrete event. Numerical results show that these vortices propagate into the fluid bulk and generate an azimuthal mean flow. Direct numerical simulations of the fluid flow in an annular container with librating outer (inner) cylinder side wall and Reynolds-averaged Navier-Stokes (RANS) equations as diagnostic equations are used to investigate generation mechanism of the retrograde (prograde) azimuthal mean flow in the bulk. First, we explain, phenomenologically, how absolute angular momentum of the bulk flow is mixed and changed due to the propagation of the G{\"o}rtler vortices, causing a new vortex of basin size. Then we investigate the RANS equations for intermediate time scale of the development of the G{\"o}rtler vortices and for long time scale of the order of several libration periods. The former exhibits sign selection of the azimuthal mean flow. Investigating the latter, we predict that the azimuthal mean flow is proportional to the libration amplitude squared and to the inverse square root of the Ekman number and libration frequency and then confirms this using the numerical data. Additionally, presence of an upscale cascade of energy is shown, using the kinetic energy budget of fluctuating flow.}, language = {en} } @phdthesis{Klein, author = {Klein, Marten}, title = {Inertial wave attractors, resonances, and wave excitation by libration : direct numerical simulations and theory}, address = {Cottbus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-41712}, pages = {273}, abstract = {Resonance phenomena are ubiquitous in Nature. Resonance means that a system can accumulate large amounts of kinetic energy. In rotating flows inertial waves provide a mechanism for resonance by redistributing momentum, kinetic energy and helicity. Kinetic energy and helicity are linked to the velocity amplitudes, whereas helicity also depends on the velocity gradients (shear) in the flow. Large values of the kinetic energy and the helicity can thus lead to instability and turbulence. In order to investigate inertial waves a Taylor-Couette system was investigated which consists of a homogeneous liquid confined between two coaxial cylinders and two rigid lids. The inner cylinder is slightly conical (frustum) to break the vertical mirror symmetry. Inertial waves were excited by two different forcing configurations: the frustum in libration and the lids together with the outer cylinder in libration. Libration means that the rotation rate of the wall is modulated with a frequency Omega and an amplitude epsilon*Omega in which epsilon is the dimensionless libration amplitude and Omega the mean rotation rate. Direct numerical simulations (DNS) were conducted with a numerical solver in terrain-following coordinates. DNS results reveal that inertial wave excitation is localised at the edges of the confinement, which is in very good agreement with recent lab measurements of Seelig [1, PhD thesis, BTU Cottbus - Senftenberg]. A model of the wave excitation mechanism was developed with the aid of boundary layer theory. The model suggests that a difference in the boundary layer mass flux (Ekman flux) excites the waves by driving an excess Ekman pumping velocity w_E at the edges. DNS results exhibit the flux difference, and simulated kinetic energy spectra K(omega) exhibit the frequency dependency K(omega) proportional to w^2_E(omega) predicted by the model. DNS results also exhibit helical vortices at the edges which are not part of the model. Conservation properties suggest that each vortex is merely a compensating phenomenon. Spectra of the kinetic energy, the dissipation rate, the helicity and the quality factor were computed in order to assess resonance conditions. Simulated resonance peaks were as narrow as Delta omega/Omega_0 similar to 0.05. There, kinetic energy increases by a factor 10-50, even though viscous forces were still rather large (Ekman number E = nu/Omega_0 (Delta r)^(-2) is approximately 1.0E-5 with nu the kinematic viscosity and Delta r the typical radial gap width). The flow patterns found at resonance were in very good agreement with the patterns obtained by lab measurements and geometric ray tracing. DNS results suggest that there are two types of resonance in rotating flows: modes and wave attractors. In contrast to a mode, a wave attractor exhibits net focusing of wave energy and occupies a finite frequency band. DNS results show that the wave attractor resonance frequency adjusts within the frequency band which suggests that wave attractors can be relevant in various applications.}, language = {en} } @inproceedings{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Map-based modelling of high-Rayleigh-number turbulent convection in planar and spherical confinements}, series = {Conference on Modelling Fluid Flow (CMFF'18), The 17th International Conference on Fluid Flow Technologies Budapest, Hungary, September 4-7, 2018}, booktitle = {Conference on Modelling Fluid Flow (CMFF'18), The 17th International Conference on Fluid Flow Technologies Budapest, Hungary, September 4-7, 2018}, pages = {8}, abstract = {High-Rayleigh-number (high-Ra) turbulent convection is studied in planar and spherical confinement geometries using the One-Dimensional turbulence (ODT) model. ODT uses stochastic mapping events to model the effect of turbulent stirring along a representative line through the turbulent flow. Here, a new implementation of ODT is used which includes radial transport, buoyancy, and position-dependent gravity. Model parameters are optimised for air in a planar confinement with Ra = 3 x 10¹⁰ . The thermal and viscous boundary layers are found in very good agreement with reference data, especially in the vicinity of the wall, but also towards the bulk. In spherical geometry, the same model parameters yield systematically thicker boundary layers compared to the references. This was observed for various radius ratios, gravity profiles and Rayleigh numbers. Nevertheless, the bulk temperature and the asymmetry of the inner and outer boundary layers are captured by ODT. The results obtained suggests that ODT is mainly applicable for Ra ̰̰> 10⁷, and that optimal model parameters depend on the radius ratio.}, language = {en} } @inproceedings{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Towards numerical simulation of the ultimate state of convection using one-dimensional turbulence modeling}, series = {International Conference on Rayleigh B{\´e}nard Convection, May 14-18, Enschede, The Netherlands, abstracts}, booktitle = {International Conference on Rayleigh B{\´e}nard Convection, May 14-18, Enschede, The Netherlands, abstracts}, pages = {1}, language = {en} } @inproceedings{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic Modeling of Passive Scalar Transport in Turbulent Channel Flows at High Schmidt Numbers}, series = {10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017}, booktitle = {10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017}, pages = {7}, language = {en} } @inproceedings{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating the Reynolds number dependency of the scalar transfer to a wall using a stochastic turbulence model}, series = {89th Annual Meeting of the International Association of Applied Mathematics and Mechanics March 19-23, 2018 Munich, Germany, Book of abstracts}, booktitle = {89th Annual Meeting of the International Association of Applied Mathematics and Mechanics March 19-23, 2018 Munich, Germany, Book of abstracts}, publisher = {GAMM}, pages = {S. 287}, language = {en} } @inproceedings{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {On Turbulent Scalar Transport at Very High Schmidt Numbers Using a Stochastic Modeling Appro}, series = {88th Annual Meeting of the International Association of Applied Mathematics and Mechanics March 6-10, 2017 Weimar, Germany, Book of abstacts}, booktitle = {88th Annual Meeting of the International Association of Applied Mathematics and Mechanics March 6-10, 2017 Weimar, Germany, Book of abstacts}, publisher = {GAMM}, pages = {357 -- 358}, language = {en} } @misc{LignellLansingerMedinaMendezetal., author = {Lignell, David O. and Lansinger, Victoria B. and Medina M{\´e}ndez, Juan Ali and Klein, Marten and Kerstein, Alan R. and Schmidt, Heiko and Fistler, Marco and Oevermann, Michael}, title = {One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application}, series = {Theoretical and Computational Fluid Dynamics}, volume = {32}, journal = {Theoretical and Computational Fluid Dynamics}, number = {4}, issn = {0935-4964}, doi = {10.1007/s00162-018-0465-1}, pages = {495 -- 520}, abstract = {The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating the Reynolds number dependency of the scalar transfer to a wall using a stochastic turbulence model}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {18}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.201800238}, pages = {2}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {17}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.201710289}, pages = {639 -- 640}, language = {en} } @misc{VinczeFenyvesiKleinetal., author = {Vincze, Miklos and Fenyvesi, Nora and Klein, Marten and Sommeria, Joel and Viboud, Samuel and Ashkenazy, Yossi}, title = {Evidence for wind-induced Ekman layer resonance based on rotating tank experiments}, series = {EPL : a letters journal exploring the frontiers of physics}, volume = {125}, journal = {EPL : a letters journal exploring the frontiers of physics}, number = {4}, issn = {1286-4854}, doi = {10.1209/0295-5075/125/44001}, pages = {1 -- 7}, abstract = {The temporal variability of wind stress acting on the ocean surface may have a significant impact on the energy transfer between the surface ocean and the abyssal ocean. In particular, the surface ocean layer is expected to deepen when the wind's frequency matches the inertial (Coriolis) frequency, through "Ekman layer resonance". Here, we report on laboratory experiments conducted in the large circular rotating tank of the LEGI Coriolis platform (13 m in diameter and 0.5 m in depth) to investigate the effect of oscillating horizontal shear imposed at the water surface. The analysis of the flow structure by means of particle image velocimetry (PIV) reveals a resonant thickening of the top Ekman layer and a marked increase in the kinetic energy of the flow occurs when the forcing frequency coincides with the Coriolis frequency of the rotating tank. The findings are in agreement with the theoretical expectations and constitute evidence for the existence of the Ekman layer resonance (or near inertial resonance) phenomenon in an ocean-like configuration.}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Map-Based Modeling of Turbulent Convection: Application of the One-Dimensional Turbulence Model to Planar and Spherical Geometries}, pages = {1}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Map-based Modeling of Turbulent Boundary Layers Subject to Rotation and Stratification}, pages = {1}, language = {en} } @misc{KleinZenkerSchmidt, author = {Klein, Marten and Zenker, Christian and Schmidt, Heiko}, title = {Small-scale resolving simulations of the turbulent mixing in confined planar jets using one-dimensional turbulence}, series = {Chemical Engineering Science}, volume = {204}, journal = {Chemical Engineering Science}, issn = {0009-2509}, pages = {186 -- 202}, language = {en} } @misc{GhasemiKleinWilletal., author = {Ghasemi, Abouzar and Klein, Marten and Will, Andreas and Harlander, Uwe}, title = {Mean flow generation by an intermittently unstable boundary layer over a sloping wall}, series = {Journal of Fluid Mechanics}, journal = {Journal of Fluid Mechanics}, number = {vol. 853}, issn = {1750-6859}, doi = {10.1017/jfm.2018.552}, pages = {111 -- 149}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating the skin friction drag across electrolytes and electrical fields using one-dimensional turbulence modeling}, series = {European Drag Reduction and Flow Control Meeting, EDRFCM 2019, March 26-29 2019, Bad Herrenalb, Germany}, journal = {European Drag Reduction and Flow Control Meeting, EDRFCM 2019, March 26-29 2019, Bad Herrenalb, Germany}, pages = {1 -- 2}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Stochastic modeling of temperature and velocity statistics in spherical-shell convection}, series = {Geophysical Research Abstracts, Vol. 21, EGU2019-2220}, journal = {Geophysical Research Abstracts, Vol. 21, EGU2019-2220}, pages = {1}, language = {en} } @misc{SchmidtKlein, author = {Schmidt, Heiko and Klein, Marten}, title = {Simulating neutrally and stably stratified turbulent Ekman flows with a stochastic turbulence model}, series = {Proc. of the 17th European Turbulence Conference (ETC17), 3-6 September 2019, Torino, Italy}, journal = {Proc. of the 17th European Turbulence Conference (ETC17), 3-6 September 2019, Torino, Italy}, pages = {1}, language = {en} } @misc{SommeriaVinczeFenyvesietal., author = {Sommeria, Joel and Vincze, Miklos and Fenyvesi, Nora and Klein, Marten and Viboud, Samuel and Ashkenazy, Yosef}, title = {Ekman layer resonance in an ocean-analog rotating tank experiment}, series = {17th European Turbulence Conference, Turin, 3 Sep 2019 - 6 Sep 2020}, journal = {17th European Turbulence Conference, Turin, 3 Sep 2019 - 6 Sep 2020}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Rayleigh-B{\´e}nard convection at low Prandtl numbers using one-dimensional turbulence modeling}, series = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, journal = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, pages = {6}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating thermal convection at low Prandtl numbers using one-dimensional turbulence}, pages = {1}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {The transition to the ultimate regime of thermal convection from a stochastic one-dimensional turbulence perspective}, series = {arXiv}, journal = {arXiv}, pages = {1 -- 11}, language = {en} } @misc{RakhiKleinMedinaMendezetal., author = {Rakhi, Rakhi and Klein, Marten and Medina M{\´e}ndez, Juan Ali and Schmidt, Heiko}, title = {One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS}, series = {Journal of Turbulence}, volume = {20}, journal = {Journal of Turbulence}, number = {8}, issn = {1468-5248}, doi = {10.1080/14685248.2019.1674859}, pages = {506 -- 543}, abstract = {The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range 250 ≤ Reb ≤ 2000 using fixed model parameters. The influence of the model parameters is analysed for Reb = 1000 and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows.}, language = {en} } @misc{StarickMedinaMendezKleinetal., author = {Starick, Tommy and Medina M{\´e}ndez, Juan Ali and Klein, Marten and Jozefik, Zoltan and Schmidt, Heiko}, title = {Zur j{\"u}ngsten Entwicklung in der Modellierung von turbulenten Verbrennungsprozessen mittels ODT}, series = {29. Deutscher Flammentag, 17-18 September 2019, Bochum, DE}, journal = {29. Deutscher Flammentag, 17-18 September 2019, Bochum, DE}, pages = {10}, abstract = {Die vorliegende Arbeit befasst sich mit den j{\"u}ngsten Entwicklungen und Anwendungen des One-Dimensional Turbulence (ODT) Modells auf reaktive Str{\"o}mungen. Bei ODT handelt es sich um ein stochastisches und abbildungsbasiertes Turbulenzmodell zur Simulation von turbulenten Str{\"o}mungen. In ODT wird das eindimensionale Rechengebiet als gedachte Linie durch das dreidimensionale Str{\"o}mungsfeld verstanden, welches in Richtung des mittleren Gradienten einer Geschwindigkeit oder anderer skalarer Felder orientiert ist. Die Besonderheit von ODT liegt in der Modellierung der turbulenten Advektion durch stochastisch auftretende Wirbelereignisse. Die molekulare Diffusion und Reaktionskinetik entlang des ODT-Rechengebietes wird mittels sich zeitlich entwickelnder, deterministischer Erhaltungsgleichungen ber{\"u}cksichtigt und vollst{\"a}ndig aufgel{\"o}st. In dieser Arbeit werden vorl{\"a}ufige ODT-Simulationsergebnisse von reaktiven Str{\"o}mungen f{\"u}r jeweilsein offenes und ein geschlossenes System vorgestellt. Essentielle Vorarbeiten, die die Vermischungeines passiven Skalars in einer planaren Strahld{\"u}se untersuchen, werden ebenfalls gezeigt. Beim offenen System handelt es sich um eine Methan/Luft Freistrahl-Flamme in einer umgebenden Str{\"o}mung aus heißen Verbrennungsgasen. Die Simulationsergebnisse werden zu Vergleichszweckenden Messungen von Cabra et al. gegen{\"u}bergestellt. Beim geschlossenen System wird die Selbstz{\"u}ndung von mageren n-Heptan Gemischen bei niedrigen Temperaturen und komplexer Reaktionskinetik betrachtet. Hierbei werden die ODT-Ergebnisse mit den Resultaten aus einer Direkten Numerischen Simulation (DNS) verglichen. In den durchgef{\"u}hrten Studien konnte gezeigt werden, dass die mittels ODT erzeugten Statistiken eine beachtlich gute {\"U}bereinstimmung mit den Vergleichsdaten aufweisen. Im Hinblick auf die reduzierte Dimensionalit{\"a}t von ODT, die Qualit{\"a}tder erzielten Ergebnisse und die erforderliche Rechenleistung, stellt ODT ein attraktives Modell zurSimulation von turbulenten und reaktiven Str{\"o}mungen dar.}, language = {de} } @misc{StarickMedinaMendezKleinetal., author = {Starick, Tommy and Medina M{\´e}ndez, Juan Ali and Klein, Marten and Jozefik, Zoltan and Schmidt, Heiko}, title = {Zur j{\"u}ngsten Entwicklung in der Modellierung von turbulenten Verbrennungsprozessen mittels ODT}, pages = {1}, language = {de} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {One-Dimensional Turbulence investigation of variable density effects due to heat transfer in a low Mach number internal air flow}, series = {International Journal of Heat and Fluid Flow}, volume = {80}, journal = {International Journal of Heat and Fluid Flow}, issn = {0142-727X}, doi = {10.1016/j.ijheatfluidflow.2019.108481}, pages = {19}, abstract = {A novel spatial formulation of the One-Dimensional Turbulence (ODT) model is applied to a vertical pipe-flow with heat transfer, analogous to the Direct Numerical Simulation (DNS) performed by Bae et al. [Phys. Fluids 18, (075102) (2006)]. The framework presented here is an extension for radially confined domains of the cylindrical ODT spatial formulation for low Mach number flows with variable density. The variable density simulations for air (Prandtl number Pr = 0.71) are performed at an initial bulk Reynolds number Reb (DNS) = 6000 and Grashof number Gr (DNS) = 6.78*10^6. ODT results are presented for both the spatial formulation introduced in this work and the standard temporal formulation for cylindrical flows introduced by Lignell et al. [Theor. Comput. Fluid Dyn. 32, 4 (2018), pp. 495-520]. Streamwise bulk profiles and radial profiles at specific streamwise positions for the temporal and spatial formulations are in good agreement with the DNS results from Bae et al. For the present application, the spatial formulation yields physically better results in comparison to the temporal formulation. Overall, the findings in the original work of Bae et al. were corroborated with ODT. Although the framework proposed in this work is not a compressible framework and has some clear limitations regarding conservation properties, we suggest its use for future studies in the low Mach number variable density regime.}, language = {en} } @misc{KurganskySeeligKleinetal., author = {Kurgansky, Michael V. and Seelig, Torsten and Klein, Marten and Will, Andreas and Harlander, Uwe}, title = {Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus}, series = {Geophysical \& Astrophysical Fluid Dynamics}, volume = {114}, journal = {Geophysical \& Astrophysical Fluid Dynamics}, number = {6}, issn = {1029-0419}, doi = {10.1080/03091929.2019.1692829}, pages = {762}, abstract = {Laboratory experiments with a rotating cylindrical annulus arereported that reveal a prograde jet, which is adjacent to a (longitu-dinally) librating inner straight cylindrical wall. Here, wall libration isrealised as a time-harmonic modulation of the inner cylinder's rota-tion rate. The outer cylindrical wall and bottom and top lids rotatewith constant angular velocity. The main purpose of our study is tocontribute to a qualitative and quantitative understanding of non-linearities that are present in oscillating, but centrifugally stable,vertical boundary layers frequently encountered in rotating wall-bounded flows. We consider a problem that is in a sense comple-mentary to that of previous works that focused on oscillating Ekmanlayers but neglected the vertical Stokes-Stewartson layers. A sim-ple analytical model is proposed that is able to predict the magni-tude and spatial structure of the emerging prograde near-wall jet interms of nonlinearity inherent in the inner cylinder's boundary layerdynamics.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of passive scalars in turbulent channel flows}, series = {Jahresbericht 2020 zum Band: Notes on Numerical Fluid Mechanics and Multidisciplinary Design - New Results in Numerical and Experimental Fluid Mechanics XIII}, volume = {2020}, journal = {Jahresbericht 2020 zum Band: Notes on Numerical Fluid Mechanics and Multidisciplinary Design - New Results in Numerical and Experimental Fluid Mechanics XIII}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {G{\"o}ttingen}, pages = {30 -- 31}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {2020}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {20}, publisher = {Wiley-VCH}, address = {Weinheim}, doi = {10.1002/pamm.202000128}, pages = {1 -- 2}, abstract = {We investigate turbulent Couette flows of dilute, weakly-conducting electrolytes by utilizing the stochastic one-dimensional turbulence (ODT) model. The flow is driven by relative motion of the top and bottom wall and affected by an electric field between these walls that is prescribed by a voltage difference. The electrolytes considered have zero bulk charge and consist of two ion species with the same mobility, valence, and initial concentration. The stochastic model predicts a decrease of the mean streamwise velocity when an external voltage is applied provided that both Schmidt (Sc) and Reynolds (Re) numbers are sufficiently large, that is, Sc > 30 for Re = 12000 investigated. The effect observed is relevant for flow control, but the mechanism awaits clarification. Present ODT results may help to develop this understanding or design laboratory experiments.}, language = {en} } @misc{SharmaKleinSchmidtetal., author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko and Sarradj, Ennes}, title = {On a lower-order framework for jet noise prediction based on one-dimensional turbulence}, series = {arXiv}, journal = {arXiv}, pages = {1 -- 4}, abstract = {Noise prediction requires the resolution of relevant acoustic sources on all scales of a turbulent flow. High-resolution direct numerical and large-eddy simulation would be ideal but both are usually too costly despite developments in high performance computing. Lower-order modeling approaches are therefore of general interest. A crucial but standing problem for accurate predictive modeling is the estimation of missing noise from the modeled scales. In this paper we address this problem by presenting a novel lower-order framework that couples the one-dimensional turbulence model to the Ffowcs-Williams and Hawkings approach for prediction of the far-field noise of a subsonic turbulent round jet.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Predictive modeling of passive scalar transfer to a wall using stochastic one-dimensional turbulence}, series = {arXiv}, journal = {arXiv}, pages = {8}, abstract = {Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the boundary layer structure and the scaling regimes, for which it is close to asymptotic one-dimensional theory.}, language = {en} } @misc{SchmidtMedinaMendezKlein, author = {Schmidt, Heiko and Medina M{\´e}ndez, Juan Ali and Klein, Marten}, title = {EHD turbulence in channel flows with inhomogeneous electrical fields: a one-dimensional turbulence study}, series = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, doi = {10.23967/wccm-eccomas.2020.131}, pages = {12}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Modeling one and two passive scalar mixing in turbulent jets using one-dimensional turbulence}, series = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, pages = {1}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {MS404: Map-based stochastic methods for accurate modeling of turbulent heat and mass transfer}, series = {14th World Congress on Computational Mechanics (WCCM XIV) ; 8th European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2020), July 19-24, 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM XIV) ; 8th European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2020), July 19-24, 2020, Paris, France}, pages = {1}, language = {en} } @misc{KleinKersteinSchmidt, author = {Klein, Marten and Kerstein, Alan R. and Schmidt, Heiko}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection}, series = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, journal = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {2}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for thermal convection with internal sources}, address = {IPAM Workshop: Transport and Mixing in Complex and Turbulent Flows (CTF2021), University of California, Los Angeles, CA, USA}, pages = {1}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Map-based stochastic methods for accurate modeling of turbulent transport: towards poly-dispersed engineering flows}, series = {Jahrestreffen der ProcessNet Fachgruppen Mehrphasenst{\"o}mung (MPH) und Computational Fluid Dynamics (CFD)}, journal = {Jahrestreffen der ProcessNet Fachgruppen Mehrphasenst{\"o}mung (MPH) und Computational Fluid Dynamics (CFD)}, address = {Cottbus}, pages = {2}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Map-based modeling of high-Ra turbulent convection in planar and spherical geometries}, series = {Conference on Modelling Fluid Flow 2018 (CMFF'18)}, journal = {Conference on Modelling Fluid Flow 2018 (CMFF'18)}, pages = {1}, abstract = {Turbulent convection is important in many technological and geophysical applications. A model problem for such flows is Rayleigh-B{\´e}nard (RB) convection. The classical RB setup is a fluid- filled box with a heated bottom and cooled top. For geophysical applications, the spherical geometry of the confinement is sometimes important (e.g. in mantle convection). This is addressed by a spherical annulus configuration in which fluid is confined between an inner hot and an outer cold sphere. In this case, the gravity field is radial and its strength can also vary with the radius. Numerical simulations of RB convection are challenging because of the high Rayleigh numbers (Ra) observed in applications. 3-D direct simulations have been performed up to Ra ~ 10^(12), but even larger values of Ra are relevant. Hence modeling is needed if one wishes to increase the accessible Rayleigh number limit within the considerable future. The difficulty is that gradient-diffusion approaches do not allow for scale interactions, which can be crucial for the dynamics of the flow and the resulting heat transfer. In order to make such simulations feasible we make use of a different modeling strategy, the so-called One-Dimensional Turbulence (ODT). ODT resolves all scales of the flow along a notional line of sight, but reduces cost by assuming statistical homogeneity of the flow in the off-line directions. Along the line, turbulent advection is modeled by discrete mapping events, which mimic the effect of turbulent stirring. These events are stochastically sampled with highest probability where shear and buoyancy yield net available energy in analogy to real turbulence. In the talk, we evaluate ODT results against available reference data (e.g. flow statistics, heat transfer) using a new and fully adaptive version of ODT. This new version allows to simulate turbulent convection in spherical geometry. We address this by discussing the effects of radius ratio and radius-dependent gravity.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Rayleigh-B{\´e}nard convection at low Prandtl numbers using one-dimensional turbulence modeling}, series = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, journal = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, pages = {1 -- 3}, abstract = {We numerically investigate the heat transfer in turbulent Rayleigh-Bénard convection at two Prandtl numbers, Pr = 0.021 and 0.7, respectively. Small-scale resolving simulations up to the Rayleigh numbers Ra = 10^(13) (Pr = 0.021) and 10^(16) (Pr = 0.7) are made feasible by utilizing the stochastic, one-dimensional turbulence (ODT) model. Present ODT simulations exhibit effective Nusselt number Nu scalings of the form Nu ∼ Ra^γ. At low Rayleigh numbers, ODT yields a scaling exponent of γ = 0.29 (Pr = 0.021) and 0.32 (Pr = 0.7), respectively. Both values are systematically, but just slightly, overestimating available reference data. At high Rayleigh numbers, present ODT results exhibit an increase of the exponent to γ = 0.32 (Pr = 0.021) and 0.36 (Pr = 0.7), respectively. Our preliminary results suggest that ODT might be able to capture a transition from the classical to the ultimate state of convection in terms of (i) critical Rayleigh number and (ii) increase of γ.}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {The One-Dimensional Turbulence Aspects of Internal Forced Convective Flows}, series = {14th WCCM-ECCOMAS Congress 2020}, journal = {14th WCCM-ECCOMAS Congress 2020}, publisher = {Scipedia}, doi = {10.23967/wccm-eccomas.2020.338}, pages = {1 -- 12}, abstract = {We present an overview of issues for the modeling of internal forced convective flows with the One-Dimensional Turbulence (ODT) model. Results of recent research as well as prospective research issues are presented for statistically streamwise homogeneous flows and streamwise inhomogeneous mixed convective flows. The results illustrate the capabilities of the model to evaluate and bring insight into a wide range of physical phenomena in the field of convective flows. Nonetheless, as a model, ODT is best suited for the evaluation of asymptotically turbulent flows, i.e., away from laminar regimes.}, language = {en} } @misc{KleinZenkerHerthaetal., author = {Klein, Marten and Zenker, Christian and Hertha, Katja and Schmidt, Heiko}, title = {Modeling One and Two Passive Scalar Mixing in Turbulent Jets Using One-Dimensional Turbulence}, series = {14th WCCM-ECCOMAS Congress 2020}, journal = {14th WCCM-ECCOMAS Congress 2020}, publisher = {Scipedia}, doi = {10.23967/wccm-eccomas.2020.205}, pages = {1 -- 12}, abstract = {Turbulent mixing of two passive scalars is investigated in a constant-property jets using stochastic one-dimensional turbulence (ODT). Scalars are separately injected by a central round and a surrounding annular jet that issue into a uniform co-flow of low velocity. These scalars are transported downstream and dispersed in radial direction by turbulent advection and molecular diffusion. The jet as well as the turbulent inflow are numerically simulated with ODT as stand-alone tool using a temporal (T-ODT) and spatial (S-ODT) formulation. We show that ODT captures key properties of the turbulent mixing for one scalar by performing individual scalar statistics and for two scalars by computation of joint probabilities. Some limitations of the one-dimensional modeling approach are also discussed.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes}, series = {91st Annual Meeting of GAMM 2020@21}, journal = {91st Annual Meeting of GAMM 2020@21}, pages = {1}, abstract = {We investigate turbulent electrohydrodynamic (EHD) Couette flows of dilute electrolytes and how they are affected by a prescribed electric field. In this canonical problem, molecular diffusion and electric drift currents can interact with turbulence which yields intricate dynamics down to the Kolmogorov and Batchelor scales that need to be resolved. The electrolytes considered have neutral bulk charge and consist of two independent, positive and negative, ion species with the same valence and mobility. The top wall of the set-up is moving and held at a different voltage relative to the bottom one. Resolution requirements and numerical feasibility are addressed by utilizing the stochastic one-dimensional turbulence (ODT) model as stand-alone tool in order to resolve all relevant scales of the flow for a dimensionally reduced setting. Deterministic diffusion and charge-carrier drift are directly resolved, whereas the effects of turbulent advection and pressure fluctuations are modeled by a stochastic process that operates along the wall-normal ODT domain. For the hydrodynamic and low Schmidt number EHD regime, ODT reasonably captures and extrapolates relevant leading-order boundary-layer properties of reference direct numerical simulations (DNS). For the high Schmidt number EHD regime, the model predicts notable interactions between turbulence and elektrokinetics only for large enough Reynolds numbers that manifests itself by a significant increase of the turbulent drag. Present ODT results suggests that the origin of this effect is related to the time-scale separation of convective versus electric drift and molecular transport processes transport across the boundary layer. In the talk, we will address the model formulation and its application to EHD Couette flow. Additionally, we will comment on the representation of electrokinetics and hydro-dynamics for the selected set-up. Finally, we will discuss the flow regimes in terms of skin friction drag and flow profiles with an eye also on electric variables and time scales.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers}, series = {91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) - PAMM, Proceedings in Applied Mathematics and Mechanics}, volume = {20}, journal = {91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) - PAMM, Proceedings in Applied Mathematics and Mechanics}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202000127}, pages = {3}, abstract = {Turbulence is a transient phenomenon in atmospheric boundary layers. These transients occur often due to surface temperature variations (e.g. due to diurnal forcing) that directly influence the near-surface flow by local stratification effects. Relevant dynamical and transport processes occur on a scale of meters near the surface which is a standing challenge for numerical weather and climate prediction. Here we investigate neutral and stably-stratified Ekman flows as a canonical problem for the night-time atmospheric boundary layer over flat terrain. The set-up used consists of an incompressible fluid over a smooth horizontal no-slip wall in a rotating frame of reference. The bulk flow is in geostrophic balance and acts as momentum source. In the case of stable stratification, temperature is prescribed as sudden cooling on a fully-developed turbulent neutrally-stratified Ekman boundary layer. When the stratification is weak, the temperature behaves like a passive scalar, but when it is strong, turbulence may locally disappear. Transient simulations across a relevant range of Reynolds and Froude numbers are made feasible by utilizing the stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve vertical (wall-normal) transport processes on all relevant scales for a one-dimensional domain. Deterministic molecular diffusion and Coriolis forces are directly resolved, whereas turbulent advection is modeled by a stochastic process. The model obeys several relevant physical principles as, for example, Richardson's 1/4 law of stratified turbulence. Preliminary results suggest that the stand-alone model generally captures Reynolds (turbulence) and Froude number (stratification) effects when stratification is weak. For low Froude number (strong stratification), these results indicate that the model tends to overestimate turbulence effects near the surface unless stratification becomes so strong that near-surface turbulence is energetically prohibited. In the talk, we will address the model formulation and its application to Ekman flow. We will show and discuss model results for surface fluxes, boundary-layer profiles, and corresponding fluctuation statistics. In addition, we will discuss stratification effects and comment on their representation in the model.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for radiatively driven turbulent convection}, series = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, journal = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, language = {en} } @incollection{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic Modeling of Passive Scalars in Turbulent Channel Flows: Predictive Capabilities of One-Dimensional Turbulence}, series = {New Results in Numerical and Experimental Fluid Mechanics XIII}, booktitle = {New Results in Numerical and Experimental Fluid Mechanics XIII}, editor = {Dillmann, Andreas and Heller, Gerd and Kr{\"a}mer, Ewald and Wagner, Claus}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-79561-0}, doi = {10.1007/978-3-030-79561-0_5}, pages = {47 -- 57}, abstract = {Numerical simulations of passive scalars in turbulent channel flows up to friction Reynolds number Reτ = 5200 and Schmidt number Sc = 2000 are performed by utilizing the stochastic one-dimensional turbulence (ODT) model as stand-alone tool. The model is calibrated once for the turbulent velocity boundary layer at Reτ = 5200 so that the passive scalar is a model prediction. ODT is able to reproduce with reasonable accuracy the scaling regimes of the scalar transfer and locally resolve the boundary layer structure. Albeit the model is unable to capture the emerging dissimilarity of near-wall scalar and momentum transport for high Sc, it can economically and accurately represent fluctuating wall-normal fluxes.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochasticmodel for thermal convection with internal sources}, pages = {1}, abstract = {It is well established that heat transfer in turbulent Rayleigh-Bénard convection and angular momentum transfer in turbulent Taylor-Couette flow are similar in nature. This similarity manifests itself by isomorphic scaling laws for corresponding flow regimes. However, it is not clear at present if this similarity extends to flows with internal sources and different types of boundary conditions. Internal sources may occur, for example, due to radiative heating in dry or condensation in moist convection, or due to internal wave breaking and mean flow excitation in rotating Taylor-Couette-like flows. In this study, heat transfer in radiatively-driven turbulent Rayleigh-Bénard convection is investigated using the stochastic one-dimensional-turbulence model (ODT). A Boussinesq fluid of Prandtl number 1 is confined between two horizontal adiabatic no-slip walls that are located at z = 0 and H, respectively. The fluid is exposed to constant background gravity that points in vertical (-z) direction. A flow is driven by radiative heating from below yielding the local heating rate Q(z) = (P/l) exp(-z/l), where P is the prescribed mean total heat flux and l the absorption length that controls the thermal boundary layer thickness. ODT resolves all relevant scales of the flow, including molecular-diffusive scales, along a vertical one-dimensional domain, whereas stochastically sampled eddy events represent the effects of turbulent advection. ODT results reproduce and extrapolate available reference experiments of Lepot et al. (Proc. Natl. Acad. Sci. USA, 115, 2018, pp. 8937-8941) and Bouillaut et al. (J. Fluid Mech., 861, 2019, R5) in particular capturing the turbulent transition from the classical to the 'ultimate' regime. For these regimes, the exponent values in N u ∼ Ra^p scaling are found to be p ≈ 0.33 and p ≈ 0.55, respectively, in agreement with measured values. Joint probabilities of turbulent eddy size and location suggest that the regime transition is associated with a suppression of small-scale near-wall turbulent motions. The latter observation is found consistent with recent direct numerical simulations of heat transfer between permeable walls (Kawano et al., J. Fluid Mech., 914, 2021, A13).}, language = {en} } @misc{KleinZenkerSchmidt, author = {Klein, Marten and Zenker, Christian and Schmidt, Heiko}, title = {Map-based stochastic modeling of turbulent mixing in transient shear flows}, series = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, journal = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, pages = {1}, abstract = {Map-based stochastic modeling distinguishes molecular-diffusive from turbulent-advective transport processes in fluid flows. In the one-dimensional turbulence (ODT) model, a stochastic point process with energetically constrained rejection sampling of discrete eddy events is used to economically model the effects of turbulence on all relevant scales of the flow. Here I will discuss the model formulation and its application to passive scalar mixing in a confined jet. [1] M. Klein, C. Zenker, H. Schmidt (2019) Chem. Eng. Sci. 204:186-202}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection, 25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {1}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers}, series = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, journal = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, doi = {10.5194/ems2021-79}, abstract = {Turbulence is ubiquitous in atmospheric boundary layers and manifests itself by transient transport processes on a range of scales. This range easily reaches down to less than a meter, which is smaller than the typical height of the first grid cell layer adjacent to the surface in numerical models for weather and climate prediction. In these models, the bulk-surface coupling plays an important role for the evolution of the atmosphere but it is not feasible to fully resolve it in applications. Hence, the overall quality of numerical weather and climate predictions crucially depends on the modeling of subfilter-scale transport processes near the surface. A standing challenge in this regard is the robust but efficient representation of transient and non-Fickian transport such as counter-gradient fluxes that arise from stratification and rotation effects. We address the issues mentioned above by utilizing a stochastic one-dimensional turbulence (ODT) model. For turbulent boundary layers, ODT aims to resolve the wall-normal transport processes on all relevant scales but only along a single one-dimensional domain (column) that is aligned with the vertical. Molecular diffusion and unbalanced Coriolis forces are directly resolved, whereas effects of turbulent advection and stratification are modeled by stochastically sampled sequence of mapping (eddy) events. Each of these events instantaneously modifies the flow profiles by a permutation of fluid parcels across a selected size interval. The model is of lower order but obeys fundamental conservation principles and Richardson's 1/4 law by construction. In this study, ODT is applied as stand-alone tool in order to investigate nondimensional control parameter dependencies of the scalar and momentum transport in turbulent channel, neutral, and stably-stratified Ekman flows up to (friction) Reynolds number Re = O(104). We demonstrate that ODT is able to capture the state-space statistics of transient surface fluxes as well as the boundary-layer structure and nondimensional control parameter dependencies of low-order flow statistics. Very good to reasonable agreement with available reference data is obtained for various observables using fixed model set-ups. We conclude that ODT is an economical turbulence model that is able to not only capture but also predict the wall-normal transport and surface fluxes in multiphysics turbulent boundary layers.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers, EMS Annual Meeting 2021, online, 6-10 Sep 2021}, pages = {1}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling and simulation of turbulent boundary layers in annular channel flow using one-dimensional turbulence}, series = {STAB Jahresbericht 2021}, volume = {2021}, journal = {STAB Jahresbericht 2021}, editor = {Wagner, Claus}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {G{\"o}ttingen}, pages = {39 -- 40}, abstract = {In our contribution to the STAB workshop we will present the ODT model formulation with an emphasis on turbulent eddy energetics and map-based advection modeling in radial direction. After that, we will address ODT's capabilities for simulation of turbulent boundary layers in planar and annular channel flows in terms of conventional turbulence statistics and bulk quantities. Last, we will address the effects of radius ratio and Reynolds number variations.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence}, series = {International Journal of Heat and Fluid Flow}, volume = {93 (2022)}, journal = {International Journal of Heat and Fluid Flow}, issn = {0142-727X}, doi = {10.1016/j.ijheatfluidflow.2021.108889}, pages = {1 -- 19}, abstract = {Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt (Sc), Reynolds (Re), and Peclet (Pe) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood (Sh) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic Sc and Re, ODT results fall between the Dittus-Boelter, Sh ∼ Re^(4/5) Sc^(2/5), and Colburn, Sh ∼ Re^(4/5) Sc^(1/3), scalings but they are closer to the former. For finite Sc and Re, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic Sc ≪ Re_τ^(-1) (diffusive limit) with a functional form that has not been previously described.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Schmidt number effects in turbulent electroconvection using one-dimensional turbulence}, series = {Proc. Appl. Math. Mech.}, volume = {21}, journal = {Proc. Appl. Math. Mech.}, publisher = {Wiley}, address = {Weinheim}, doi = {https://doi.org/10.1002/pamm.202100147}, pages = {1 -- 3}, abstract = {Turbulent electroconvection denotes a fluctuating multiphysical flow in which hydrodynamics and electrokinetics interact on multiple scales. The dynamical processes at work are entangled down to the molecular-diffusive scales that are determined by the Schmidt (Sc) and Reynolds (Re) number. Turbulence properties are generally nonuniversal which leads to high numerical resolution requirements. We address the numerical challenges associated with accuracy and feasibility by utilizing a stochastic one-dimensional turbulence (ODT) model. Here, ODT is applied to turbulent Couette flow of dilute electrolytes as canonical problem for turbulent electroconvection. For Sc ⩾ O(10), ODT predicts an increase of the skin friction drag due to electrohydrodynamically (EHD) enhanced small-scale eddy production once the flow is sufficiently turbulent.}, language = {en} } @misc{KleinMaierSchmidt, author = {Klein, Marten and Maier, Roland Erich and Schmidt, Heiko}, title = {Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers}, series = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, volume = {21}, journal = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, publisher = {Wiley}, address = {Weinheim}, doi = {10.1002/pamm.202100146}, pages = {1 -- 3}, abstract = {Neutral and stably-stratified Ekman boundary layers (EBLs) are numerically investigated with a stochastic one-dimensional turbulence (ODT) model. EBLs achieve the bulk-surface coupling in Earth's atmosphere. They are numerically challenging due to transient and non-universal turbulence properties even at small scales. ODT addresses this problem by distinguishing turbulent-advective from molecular-diffusive transport processes for a vertical column along which all relevant scales of the flow are resolved. We demonstrate the model's capabilities for economical, accurate, and stratification regime independent simulation of EBLs for the wind-turning angle. ODT reproduces and extrapolates reference direct numerical simulation results consistent with observations. We conclude that ODT may be useful for modeling of atmospheric surface layers.}, language = {en} } @misc{KleinFreireLignelletal., author = {Klein, Marten and Freire, Livia S. and Lignell, David O. and Kerstein, Alan R. and Schmidt, Heiko}, title = {Ein stochastischer Ansatz zur Modellierung fluktuierender Oberfl{\"a}chenfl{\"u}sse in turbulenten Grenzschichten}, series = {Kurzfassungen der Meteorologentagung DACH}, volume = {2022}, journal = {Kurzfassungen der Meteorologentagung DACH}, publisher = {Copernicus}, doi = {10.5194/dach2022-22}, pages = {1 -- 1}, abstract = {Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskr{\"a}fte ber{\"u}cksichtigt werden k{\"o}nnen. Das Modell wird beispielhaft als unabh{\"a}ngiges, numerisches Werkzeug angewendet, um fluktuierende Oberfl{\"a}chenfl{\"u}sse in turbulenten Kanalstr{\"o}mungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (por{\"o}se) Oberfl{\"a}chen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberfl{\"a}chennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitteraufl{\"o}sung zu verringern.}, language = {de} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence}, series = {AIAA AVIATION 2021 FORUM}, journal = {AIAA AVIATION 2021 FORUM}, publisher = {American Institute of Aeronautics and Astronautics, Inc.}, isbn = {978-1-62410-610-1}, doi = {10.2514/6.2021-2104}, language = {en} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study}, series = {Physics of Fluids}, volume = {34}, journal = {Physics of Fluids}, number = {8}, issn = {1089-7666}, doi = {10.1063/5.0101270}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of transient Ekman flow at arbitrary Reynolds number driven by horizontal bottom wall oscillation}, series = {EMS Annual Meeting 2022, Abstracts}, volume = {19}, journal = {EMS Annual Meeting 2022, Abstracts}, publisher = {Copernicus}, address = {Bonn, Germany}, doi = {10.5194/ems2022-617}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {92nd Annual Meeting of GAMM}, journal = {92nd Annual Meeting of GAMM}, publisher = {Gesellschaft f{\"u}r angewandte Mathematik und Mechanik e.V.}, address = {Aachen, Germany}, language = {en} } @misc{KleinTsaiSchmidt, author = {Klein, Marten and Tsai, Pei-Yun and Schmidt, Heiko}, title = {Stochastic modeling of heat and momentum transfer in annular pipe flow: A one-dimensional turbulence study with comparison to DNS and LES}, series = {STAB Jahresbericht 2022}, volume = {23}, journal = {STAB Jahresbericht 2022}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using one-dimensional turbulence}, series = {Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Conference on Modelling Fluid Flow (CMFF'22)}, address = {Budapest, Hungary}, pages = {1 -- 8}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using One-Dimensional Turbulenc}, series = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, editor = {Vad, Janos}, publisher = {University of Technology and Economics, Department of Fluid Mechanics}, address = {Budapest, Hungary}, isbn = {978-963-421-881-4}, pages = {82 -- 91}, abstract = {The joint modeling of flow hydrodynamics and electrokinetics is a relatively unexplored area of turbulent flow research. We address a lack of available models for electrohydrodynamic (EHD) turbulent flow utilizing a lower-order approach, the stochastic One-Dimensional Turbulence (ODT) model. ODT is constructed on the principles of the direct energy cascade of Navier-Stokes turbulence, with key emphasis on the accurate resolution of the small molecular transport scales within a notional line-of-sight. We investigate two canonical flow configurations to demonstrate the applicability of the model in the simulation of EHD flows. First, we investigate EHD effects in zero-pressure-gradient turbulent boundary layers by two-way coupled model application to plane Couette flow of a dilute electrolyte. Second, we apply the one-way coupled model to EHD-enhanced gas flow through a vertical pipe with an inner concentric electrode, where electric fields are generated by means of a corona discharge and the corresponding effect of a continuum ionic charge density field.}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of three-scalar mixing in a coaxial jet using one-dimensional turbulence}, series = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, journal = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, pages = {1 -- 6}, abstract = {Modeling complex mixing processes is a standing challenge for a number of applications ranging from chemical to mechanical and environmental engineering. Here, the gas-phase turbulent mixing in a three-stream concentric coaxial jet is investigated as a canonical problem. Reynolds-averaged Navier-Stokes simulations (RANS) suggest that the gas-phase mixing can be accurately modeled by air doped with passive scalars, for which small-scale resolving numerical simulations are performed with the one-dimensional turbulence (ODT) model as stand-alone tool. We show that both the spatial (S-ODT) and temporal (T-ODT) model formulations yield qualitatively similar results exhibiting reasonable to good agreement with available reference experiments, Reynolds-averaged and large-eddy simulations, as well as mixing models. This is demonstrated for low-order statistics, like the scalar variance and dissipation, but also the two-scalar joint probability density functions that can not be obtained with RANS. Our results suggest that S-ODT has better capabilities than T-ODT to model the mixing processes in the jet which we attribute to the account of local advective time scales.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model}, series = {Advances in Science and Research}, volume = {19/2022}, journal = {Advances in Science and Research}, issn = {1992-0636}, doi = {10.5194/asr-19-117-2022}, pages = {117 -- 136}, abstract = {Small-scale processes in atmospheric boundary layers are typically not resolved due to cost constraints but modeled based on physical relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed in the present study with the aid of the one-dimensional turbulence (ODT) model. ODT is applied as stand-alone column model to numerically investigate stratification effects in long-lived transient Ekman flows as canonical example of polar boundary layers by resolving turbulent winds and fluctuating temperature profiles on all relevant scales of the flow. We first calibrate the adjustable model parameters for neutral cases based on the surface drag law which yields slightly different optimal model set-ups for finite low and moderate Reynolds numbers. For the stably stratified cases, previously calibrated parameters are kept fixed and the model predictions are compared with various reference numerical simulations and also observations by an exploitation of boundary layer similarity. ODT reasonably captures the temporally developing flow for various prescribed stratification profiles, but fails to fully capture the near-surface laminarization by remaining longer in a fully developed turbulent state, which suggests preferential applicability to high-Reynolds-number flow regimes. Nevertheless, the model suggests that large near-surface turbulence scales are primarily affected by the developing stratification due to scale-selective buoyancy damping which agrees with the literature. The variability of the wind-turning angle represented by the ensemble of stratified cases simulated covers a wider range than reference reanalysis data. The present study suggests that the vertical-column ODT formulation that is highly resolved in space and time can help to accurately represent multi-physics boundary-layer and subgrid-scale processes, offering new opportunities for analysis of very stable polar boundary layer and atmospheric chemistry applications.}, language = {en} } @misc{SchmidtKlein, author = {Schmidt, Heiko and Klein, Marten}, title = {Chair of Numerical Fluid and Gas Dynamics}, pages = {1}, language = {en} } @misc{HartmannKoehlerSchmidtetal., author = {Hartmann, Carsten and K{\"o}hler, Ekkehard and Schmidt, Heiko and Klein, Marten}, title = {Scientific computing LAB (SCL)}, series = {"Get Into Energy", BTU Cottbus-Senftenberg, ZHG Building, 1 Feb. 2023}, journal = {"Get Into Energy", BTU Cottbus-Senftenberg, ZHG Building, 1 Feb. 2023}, address = {Cottbus}, pages = {1}, abstract = {KEY COMPETENCE AND FOCUS • Development of numerical methods and algorithms for multi-energy systems • Multiscale and multiphysics modeling and simulation of P2X technologies • Stochastic simulation and efficient optimization of complex energy networks}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling of heated turbulent coaxial pipe flow prescribing different thermal boundary conditions}, series = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, journal = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, address = {Valencia}, pages = {1}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Fractal roughness representation in a stochastic one-dimensional turbulence modeling approach}, series = {Book of Abstracts 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, journal = {Book of Abstracts 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, address = {Montr{\´e}al, Canada}, pages = {3}, language = {en} } @misc{NaikBuryeMedinaMendezKleinetal., author = {Naik Burye, Nishidh Shailesh and Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Revisiting near-wall modeling of fully developed turbulent flow in concentric annuli}, series = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, journal = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg}, pages = {174 -- 175}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Numerical study on the effects of transient pressure gradients on isothermal and heated pipe flows}, series = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, journal = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, address = {Magdeburg (Germany)}, pages = {227 -- 228}, language = {en} } @misc{JoshiMedinaMendezKleinetal., author = {Joshi, Abhishek and Medina Mendez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Simulating homogenous isotropic turbulence with deterministic and stochastic forcings using a one-dimensional turbulence model}, pages = {1}, abstract = {To understand the intermittency present in scalar fields we need to address the expense of current start-of-art DNS to probe the higher-order structure functions. These higher order moments become increasingly sensitive to increasing Reλ and much more prone to extreme events. Here, in this work, we investigate using a Reduced order model(ODT) to simulate Homogenous Isotropic turbulence as an initial step towards that goal by employing a linear forcing [1] proposed by Lundgren that is proportional to local and instantaneous velocity.}, language = {en} } @misc{MarinkovićMedinaMendezSchmidtetal., author = {Marinković, Pavle and Medina M{\´e}ndez, Juan Ali and Schmidt, Heiko and Klein, Marten}, title = {Ongoing development of a hybrid reduced order stochastic/LES solver for turbulent flows}, address = {Cottbus}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling and theoretical analysis of heated concentric coaxial pipes at low Prandtl number}, series = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, journal = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, publisher = {GAMM e.V.}, address = {Magdeburg}, pages = {11}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Time-resolved simulations of wind speed fluctuations across atmospheric boundary layers using a stochastic forward model}, series = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, journal = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, publisher = {Deutsche Physikalische Gesellschaft (DPG)}, address = {Dresden}, abstract = {Atmospheric boundary layers (ABLs) govern the atmosphere-surface coupling and are therefore of fundamental relevance for Earth's weather and climate system. Time-resolved numerical simulations of ABLs are challenging due to intricate interactions of inertial, Coriolis, buoyancy, and viscous forces on all relevant scales of the turbulent flow. Small-scale processes, albeit potentially nonuniversal, are typically not resolved due to cost constraints but modeled based on physically justified relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed here by utilizing a dimensionally reduced stochastic modeling approach. The model aims to reproduce turbulent cascade phenomenology by a stochastic process, respecting fundamental physical conservation principles. Momentary wind velocity and temperature profiles evolve autonomously in time for an ensemble of initial conditions. By comparison with available high-fidelity reference numerical simulations, reanalysis, and observations, it is shown that the model captures various relevant flow properties, exhibiting limitations mainly in a delayed relaminarization under very stable conditions. Forthcoming research aims to contribute to a better understanding of polar boundary layers, requiring predictive modeling capabilities, high resolution, and numerical efficiency to perform long-time simulations.}, language = {de} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {22}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202200272}, abstract = {Simultaneous momentum and passive scalar transfer in weakly heated pressure-driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one-dimensional turbulence (ODT) model,which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725,2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner-outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall-function-based approaches.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0125514}, abstract = {Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock-turbulence interaction}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0137435}, abstract = {One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock-turbulence interaction cases involving Richtmyer-Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., "Simulation of shock-turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence," Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.}, language = {en} } @misc{KleinSchoepsMedinaMendezetal., author = {Klein, Marten and Sch{\"o}ps, Mark Simon and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Numerical simulation and analysis of transient Ekman boundary layers using a stochastic turbulence model}, series = {EGU General Assembly 2023}, journal = {EGU General Assembly 2023}, publisher = {EGU - European Geophysical Union}, address = {Vienna, Austria}, doi = {10.5194/egusphere-egu23-9116}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {ODT augmented RaNS}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {368}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Al{\´i} and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Towards the use of a reduced order and stochastic turbulence model for assessment of far-field sound radiation: low Mach number jet flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {413 -- 414}, language = {en} } @misc{SharmaAytonKleinetal., author = {Sharma, Sparsh and Ayton, Lorna and Klein, Marten and Schmidt, Heiko}, title = {Estimation of ODT-resolved acoustic sources in high Reynolds number turbulent jets}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {414 -- 415}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {SGS modeling in lattice Boltzmann method for non-fully resolved turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {363 -- 364}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Effects of Reynolds number on turbulent concentric coaxial pipe flow using stochastic modeling}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {365}, language = {en} } @misc{Klein, author = {Klein, Marten}, title = {Map-based stochastic modeling of multiscale transfer processes in turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {362}, abstract = {The detailed modeling of turbulent mixing has remained a numerical challenge for a number of applications, ranging from chemically reacting flows to noise prediction in technical flows, and encompassing convection on multiple scales in the geophysical context, among others. Complications arise from the dynamical complexity of turbulence that manifests itself by emergent small-scale flow features, scaling cascades, and intermittency due to prescribed forcings, boundary and initial conditions. In order to robustly predict, for example, the occurrence of catalytic reactions, generation of mixing noise, or the heat transfer across a layer of fluid, it is crucial to represent the physical redistribution processes in the flow with a proper account of participating time and length scales. This yields scale-locality and causality constraints that can usually only be fully addressed by direct numerical simulation (DNS) based on the discretized three-dimensional (3-D) Navier-Stokes equations, which is a very costly undertaking and limited to moderate or low turbulence intensities. In order to over- come the fundamental limitations of statistical turbulence models and numerical cost of DNS, so-called map-based stochastic turbulence models have been developed and increasingly applied to various mutiphysical flows over the last couple of decades. These models utilize onedimensional (1-D) generalized Baker's maps in order to distinguish advective filamentation from molecular diffusion processes, resolving all relevant scales of the flow along a single physical coordinate. Baker's maps are probabilistically sampled with respect to size, location, and time of occurrence which introduces dynamical complexity into the bottom-up modeling approach. When the sampling is based on the evolving flow state, a self-contained reduced- order model with predictive capabilities for turbulent flows can be formulated. In the talk, I will summarize the map-based stochastic modeling strategy with an emphasize on the so-called One-Dimensional Turbulence (ODT) model. After that, I will discuss some recent advances in the field, demonstrating the applicability of the approach across flow configurations. I will address in more detail the flow physics representation by means of entrainment and passive scalar mixing in turbulent jets, as well as heat flux and wall shear stress fluctuations in heated channels and stably-stratified atmospheric boundary layers.}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {Stochastic deconvolution of wall statistics in Reynolds-averaged Navier-Stokes simulations based on one-dimensional turbulence}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {23}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300055}, pages = {9}, abstract = {Reynolds-averaged Navier-Stokes simulation (RaNS) is state-of-the-art for numerical analysis of complex flows at high Reynolds number. Standalone RaNS may yield a reasonable estimate of the wall-shear stress and turbulent drag if a proper wall-function is prescribed, but detailed turbulence statistics cannot be obtained, especially at the wall. This lack in modeling is addressed here by a stochastic deconvolution strategy based on a stochastic one-dimensional turbulence (ODT) model. Here, a one-way coupling strategy is proposed in which a forcing term is computed from the balanced RaNS solution that is in turn utilized in the ODT model. The temporally developing ODT solution exhibits turbulent perturbations but relaxes toward the local RaNS solution due to resolved molecular-diffusive processes. It is demonstrated that the approach is able to recover the distribution of positive wall-shear stress fluctuations in turbulent channel flow. When formulated as post-processing tool, it is suggested that RaNS can be enhanced by ODT providing economical means for local high-fidelity numerical modeling based on a low-fidelity flow solution.}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Investigating dissipative roughness effects on turbulent drag using a stochastic turbulence model}, series = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, journal = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, address = {Valencia}, pages = {1}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Ali and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Toward the use of a reduced-order and stochastic turbulence model for assessment of far-field sound radiation: Low Mach number jet flows}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300186}, pages = {9}, language = {en} } @misc{KleinKesslerSchmidt, author = {Klein, Marten and Kessler, Robert William and Schmidt, Heiko}, title = {On the influence of a wavy leading edge on the aerodynamic drag of a wing: A numerical parameter study}, series = {STAB Jahresbericht 2023}, volume = {21/2023}, journal = {STAB Jahresbericht 2023}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, pages = {110 -- 111}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating heat transfer properties of tubular heat exchangers with a stochastic turbulence model}, series = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, journal = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, address = {Cottbus, Germany}, pages = {2}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Features of turbulent boundary layers in heated concentric coaxial pipe flow at high Reynolds and low Prandtl numbers}, series = {ICTAM 2024}, journal = {ICTAM 2024}, address = {Daegu, South Korea}, doi = {10.13140/RG.2.2.30075.12323}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating Prandtl number effects in heated concentric coaxial pipe flow at high Reynolds number}, series = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, journal = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, address = {Aachen, Germany}, pages = {1}, language = {en} }