Sensitivity of mixing efficiency to resolution of the buoyancy scale in large-eddy simulations of stratified turbulence

Mixing efficiency is studied in large-eddy simulations (LES) of stratified turbulence when the grid spacing $\Delta$ varies from being $< \sim L_b$ to $\gg L_b$, where $L_b$ is the buoyancy scale. It is shown that the irreversible mixing efficiency $\gamma$ is fairly close to that resulted from direct numerical simulations (DNS) if the buoyancy scale $L_b$ is well resolved in LES. Also, when the buoyancy scale is resolved, the vertical length scale $\mathcal{L}_v \sim L_b$, and we can scale $\gamma$ as a function of the vertical Froude number $Fr_v$ and turbulent Prandtl number $Pr_t$. If we assume $Pr_t \approx 1$, in the regime of stratified turbulence where the horizontal Froude number $Fr_h \ll 1$ and $Fr_v \sim 1$, $\gamma$ goes to a constant value $1/3$. This value of $\gamma$ has been recently reported as an upper bound of mixing efficiency in the deep ocean stratified regions near topographies. Overall, our work suggests that similar results to those from DNS approach can be yielded in LES of stratified turbulence, while the computational costs are significantly decreased in LES in comparison with expensive DNS runs.