Mixing efficiency in large-eddy simulations of stratified turbulence

Abstract

The irreversible mixing efficiency is studied using large-eddy simulations (LES) of stratified turbulence, where three different subgrid-scale (SGS) parameterizations are employed. For comparison, direct numerical simulations (DNS) and hyperviscosity simulations are also performed. In the regime of stratified turbulence where$Fr_{v}\sim 1$, the irreversible mixing efficiency$\unicode[STIX]{x1D6FE}_{i}$in LES scales like$1/(1+2Pr_{t})$, where$Fr_{v}$and$Pr_{t}$are the vertical Froude number and turbulent Prandtl number, respectively. Assuming a unit scaling coefficient and$Pr_{t}=1$,$\unicode[STIX]{x1D6FE}_{i}$goes to a constant value$1/3$, in agreement with DNS results. In addition, our results show that the irreversible mixing efficiency in LES, while consistent with this prediction, depends on SGS parameterizations and the grid spacing$\unicode[STIX]{x1D6E5}$. Overall, the LES approach can reproduce mixing efficiency results similar to those from the DNS approach if$\unicode[STIX]{x1D6E5}\lesssim L_{o}$, where$L_{o}$is the Ozmidov scale. In this situation, the computational costs of numerical simulations are significantly reduced because LES runs require much smaller computational resources in comparison with expensive DNS runs.