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dc.contributor.authorKhani, Sina 13:22:08 (GMT) 13:22:08 (GMT)
dc.description.abstractDirect 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 $\Delta$ 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 $\Delta$, below which the dynamics of stratified turbulence, including Kelvin-Helmholtz instabilities, are captured. This criterion on $\Delta$ depends on the buoyancy scale $L_b$ and varies with different SGS models: the Kraichnan model requires $\Delta/L_b < 0.47$, the Smagorinsky model requires $\Delta/L_b < 0.17$ and the dynamic Smagorinsky model requires $\Delta/ L_b < 0.24$. In addition, the statistics of the dynamic Smagorinsky coefficient $c_s$ demonstrate that large 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 the dynamics of SGS motions dramatically if the filter scale $\Delta$ 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 $Re_b \lesssim \mathcal{O}(1)$, the kinetic energy transfer shows some spectral backscatter at intermediate scales that is due to viscous effects and not to the turbulent mechanism.en
dc.publisherUniversity of Waterlooen
dc.subjectDirect numerical simulationsen
dc.subjectLarge eddy simulationsen
dc.subjectEffective eddy viscosityen
dc.subjectTurbulence modellingen
dc.subjectStratified turbulenceen
dc.subjectUpscale and downscale energy transferen
dc.titleLarge eddy simulations and subgrid scale motions in stratified turbulenceen
dc.typeDoctoral Thesisen
dc.subject.programApplied Mathematicsen Mathematicsen
uws-etd.degreeDoctor of Philosophyen

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