@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} }