@phdthesis{Klein2016, author = {Klein, Marten}, title = {Inertial wave attractors, resonances, and wave excitation by libration : direct numerical simulations and theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-41712}, school = {BTU Cottbus - Senftenberg}, year = {2016}, 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. 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 fixed amplitude and frequency of the order of 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 laboratory measurements of Seelig (2014, 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 at the edges. The DNS results exhibit this flux difference, and the simulated kinetic energy spectra of the waves exhibit the frequency dependency predicted by the model. However, DNS results also exhibit helical vortices at the edges which are not part of the model. Conservation properties suggest that these vortices are merely a compensating phenomenon which tends to stabilise the boundary layer flow. The details of this flow, however, appear less important for the wave excitation. Response 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 have a width of only 1/20th of the mean rotation rate. At these peaks, the kinetic energy was found to increase by a factor 10-50 even though viscous forces were still rather large (Ekman number of the order 1/100,000 with the length scale given by the mean radial gap width). The flow patterns found at those resonances were investigated and found to be in very good agreement with the spatial patterns obtained by laboratory measurements and geometric ray tracing. The 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 attractor resonances complement 'classical' mode resonances and may, thus, be relevant in various applications.}, subject = {Direct Numerical Simulations; Rotating flows; Resonance; Inertial waves; Boundary layer theory; Direkte Numerische Simulationen; Rotierende Str{\"o}mungen; Resonanz; Tr{\"a}gheitswellen; Grenzschichttheorie; Direkte numerische Simulation; Rotationsstr{\"o}mung; Tr{\"a}gheitswelle; Taylor-Couette-Str{\"o}mung}, language = {en} }