@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} }