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Subgrid-Scale Parameterizations And The Resolution Of Physical Scales In Large-Eddy Simulations Of Stratified Turbulence

Speaker: Sina Khani, AOS, Princeton University
Series: Special Seminars
Location: Engineering Quad E219
Date/Time: Monday, May 13, 2019, 11:00:00 a.m. - 12:00:00 p.m.

Abstract:

The computational costs and memory usage in direct numerical simulation (DNS) are indeed very high in realistic atmospheric and oceanic flows because there is a wide range of motions from large forcing scales O(500) km to small dissipation scales O(~1) mm. An alternative numerical approach is large-eddy simulation (LES), in which only large energy-containing eddies of the turbulence are directly resolved and the effects of smaller-scale motions are parameterized using subgrid-scale (SGS) models.

This seminar will have two main parts. In the first part, I present LES results of stratified turbulence when three common SGS models (i.e. the Smagorinsky, dynamic Smagorinsky and Kraichnan models) are employed. It is shown that if the grid spacing Δ is small enough, the fundamental characteristics of stratified  turbulence, including Kelvin-Helmholtz instabilities, are well-captured by LES  approach. Our results suggest that there is a maximum threshold on Δ that depends on the buoyancy scale Lb and the employed SGS model. When Δ is larger than this threshold, LES fails, while LES can reproduce DNS results if Δ is below this threshold. In the second part, I provide a theoretical scale analysis to estimate the irreversible mixing efficiency γi in LES of stratified turbulence. I show that in the regime of stratified turbulence, γi scales like 1/(2Prt+1), where Prt is the turbulent Prandtl number. Assuming Prt=1 and a unit scale coefficient, γi goes to a constant value 1/3, which is in line with DNS results. Overall, LES can reproduce the irreversible mixing efficiency similar to that in DNS when Δ < Lo, where Lo is the Ozmidov scale. In both cases, the computational costs are significantly reduced because LES requires much smaller computational resources in comparison with DNS.

At the end of my talk, I will also briefly discuss about the implication of this work to study the energy transfer and scale interactions in a wide range of motions in atmospheric and oceanic flows.