Inertial wave attractors, resonances, and wave excitation by libration : direct numerical simulations and theory

Trägheitswellenattraktoren, Resonanzen und deren Anregung durch Libration : direkte numerische Simulationen und Theorie

  • 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 epsilonResonance 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.show moreshow less

Export metadata

Additional Services

Search Google Scholar
Metadaten
Author: Marten KleinORCiD
URN:urn:nbn:de:kobv:co1-opus4-41712
Place of publication:Cottbus
Document Type:Doctoral thesis
Language:English
Year of publication:2016
Tag:Boundary Layer Theory; Direct Numerical Simulation; Ekman boundary layer; Fluid Mechanics; Inertial Wave; Libration; Resonance in Fluids; Rotation; Wave Attractor; Wave focusing
Number of pages:273
Faculty/Chair:Fakultät 2 Umwelt und Naturwissenschaften / FG Atmosphärische Prozesse
Einverstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.