TY - GEN A1 - Kurgansky, Michael V. A1 - Seelig, Torsten A1 - Klein, Marten A1 - Will, Andreas A1 - Harlander, Uwe T1 - Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus T2 - Geophysical & Astrophysical Fluid Dynamics N2 - 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. KW - boundary layer structure KW - geophysical and geological flows KW - longitudinal libration Y1 - 2020 U6 - https://doi.org/10.1080/03091929.2019.1692829 SN - 1029-0419 VL - 114 IS - 6 SP - 762 ER - TY - GEN A1 - Ghasemi, Abouzar A1 - Klein, Marten A1 - Harlander, Uwe A1 - Kurgansky, Michael V. A1 - Schaller, Eberhard A1 - Will, Andreas T1 - Mean flow generation by Görtler vortices in a rotating annulus with librating side walls T2 - Physics of Fluids N2 - 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 Görtler 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 Görtler vortices, causing a new vortex of basin size. Then we investigate the RANS equations for intermediate time scale of the development of the Görtler 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. KW - Direct Numerical Simulation KW - Fluid Mechanics KW - Mean Flow KW - Rotation KW - Cylinder KW - Centrifugal KW - Instability KW - Mechanism KW - Vortex Y1 - 2016 U6 - https://doi.org/10.1063/1.4948406 VL - 28 IS - 056603 SP - 1 EP - 23 ER - TY - CHAP A1 - Klein, Marten A1 - Ghasemi, Abouzar A1 - Seelig, Torsten A1 - Borcia, Ion-Dan A1 - Harlander, Uwe A1 - Will, Andreas T1 - Mean flow generation and inertial wave attractors in a librating annulus: DNS and theory T2 - European Geosciences Union, General Assembly 2015, Vienna, Austria, 13 April - 17 May 2015 KW - boundary-layer structure KW - direct numerical simulation KW - instability KW - waves in rotating fluids Y1 - 2015 UR - http://meetingorganizer.copernicus.org/EGU2015/EGU2015-15640-1.pdf N1 - EGU2015-15640-1 PB - European Geophysical Society CY - Katlenburg-Lindau ER - TY - CHAP A1 - Klein, Marten A1 - Borcia, Ion-Dan A1 - Egbers, Christoph A1 - Ghasemi, Abouzar A1 - Harlander, Uwe A1 - Kurgansky, Michael V. A1 - Schaller, Eberhard A1 - Seelig, Torsten A1 - Will, Andreas T1 - Inertial Waves and Wave Excitation Mechanisms in Annular Cavities: Simulations, Experiments and Theory T2 - European Turbulence Conference ETC14, Lyon, 2013 KW - boundary-layer structure KW - geophysical and geological flows KW - waves in rotating fluids Y1 - 2013 UR - http://etc14.ens-lyon.fr/etc-14-proceedings/accepted-talks ER - TY - CHAP A1 - Klein, Marten A1 - Ghasemi, Abouzar A1 - Harlander, Uwe A1 - Will, Andreas T1 - Inertial wave excitation and wave attractors in a librating annulus: DNS T2 - European Geosciences Union, General Assembly 2014, Vienna, Austria, 27 April – 02 May 2014 KW - boundary-layer structure KW - geophysical and geological flows KW - waves in rotating fluids KW - direct numerical simulations Y1 - 2014 N1 - EGU2014-15585 PB - European Geophysical Society CY - Katlenburg-Lindau ER - TY - GEN A1 - Klein, Marten A1 - Seelig, Torsten A1 - Kurgansky, Michael V. A1 - Ghasemi, Abouzar A1 - Borcia, Ion-Dan A1 - Will, Andreas A1 - Schaller, Eberhard A1 - Egbers, Christoph A1 - Harlander, Uwe T1 - Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder T2 - Journal of Fluid Mechanics N2 - 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 Poincaré 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. KW - boundary-layer structure KW - geophysical and geological flows KW - waves in rotating fluids Y1 - 2014 U6 - https://doi.org/10.1017/jfm.2014.304 SN - 1750-6859 IS - vol. 751 SP - 255 EP - 297 ER - TY - CHAP A1 - Klein, Marten A1 - Ghasemi, Abouzar A1 - Seelig, Torsten A1 - Borcia, Ion-Dan A1 - Harlander, Uwe A1 - Will, Andreas T1 - DNS of inertial wave attractors in a librating annulus with height-dependent gap width T2 - 15th European turbulence conference (ETC), Delft, The Netherlands (2015) N2 - 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. KW - direct numerical simulations KW - geophysical and astrophysical turbulence KW - waves in rotating fluids Y1 - 2015 UR - http://www.etc15.nl/proceedings/proceedings/documents/134.pdf ER - TY - CHAP A1 - Klein, Marten A1 - Ghasemi, Abouzar A1 - Seelig, Torsten A1 - Borcia, Ion-Dan A1 - Harlander, Uwe A1 - Will, Andreas T1 - DNS of inertial wave attractors in a librating annular cavity with a height-dependent gap T2 - ICTW 19, Book of Abstracts, 19th International Couette-Taylor Workshop, June 24 - 26, 2015 Cottbus, Germany KW - waves in rotating fluids KW - geophysical and geological flows KW - direct numerical simulations Y1 - 2015 SP - 122 EP - 123 CY - Cottbus ER -