Sina Khani | Applied Math, University of Waterloo
Large eddy simulations and subgrid scale motions in stratified turbulence
Direct numerical and large eddy simulations (DNS & LES) of decaying and forced stratified turbulence are studied in this thesis. By defining a test filter scale k_c in the horizontal and vertical directions separately, the energy transfer spectra are investigated. It is shown that stratification affects the horizontal eddy viscosity significantly, by which the non-local energy transfer between large and small horizontal scales are increased. This non-local horizontal energy transfer is around 20% of the local horizontal energy transfer at the cutoff wavenumber k_c. In addition, the non-local horizontal energy transfer occurs at large vertical wavenumbers, including the buoyancy wavenumber k_b =N⁄u_rms , where N is the buoyancy frequency and u_rms is the root-mean-square velocity. The non-local horizontal eddy viscosity decreases and the local eddy viscosity is dominant if the value of the test cutoff k_c varies from large scales to the dissipation scales. Next, the performance of three common subgrid scale (SGS) models, i.e. the Kraichnan, Smagorinsky and dynamic Smagorinsky models, is investigated in stratified turbulence. It is shown that if the grid spacing Δ is small enough, the horizontal wavenumber spectra show an approximately (-5)⁄3 slope along with a bump at the buoyancy wavenumber k_b. Our results suggest that there is a maximum threshold on Δ, below which the dynamics of stratified turbulence, including Kelvin-Helmholtz instabilities, are captured. This criterion on Δ depends on the buoyancy scale L_b and varies with different SGS models: the Kraichnan model requires Δ⁄L_b<0.47 , the Smagorinsky model requires Δ⁄L_b<0.17 and the dynamic Smagorinsky model requires Δ⁄L_b<0.24. In addition, the statistics of the dynamic Smagorinsky coefficient c_s demonstrate that larger shear leads to small values of c_s in stratified turbulence (in line with the results for isotropic turbulence). Finally, it is shown that the net down-scale energy transfer in stratified turbulence is a combination of two large values of upscale and downscale energy transfer mechanisms. Overall, our results suggest that stratification changes dynamics of SGS motions dramatically if the filter scale Δ is around the Ozmidov scale or smaller; in order to capture the dynamical features of stratified turbulence, LES requires resolution of L_b. In addition, when the buoyancy Reynolds number Re_b≾ O(1), the kinetic energy transfer shows some spectral backscatter at intermediate scales that is due to viscous effects and not to the turbulent mechanism.