Stochastic backscatter in large eddy simulations of decaying stratified turbulence

This paper assesses the potential of the Leith stochastic backscatter model in large eddy simulations (LES) of decaying homogeneous stratified turbulence. LES with Smagorinsky eddy viscosity and different values of the Leith backscatter parameter Cb are compared to one another and to direct numerical simulations (DNS) for two strong stratifications. For a small Leith parameter Cb=0.1, positive (dissipation) values of the sub-filter energy transfer are in good agreement with the DNS, while negative (backscatter) values are somewhat under-predicted for the lower stratification and in better agreement with DNS for the higher stratification. The resulting kinetic energy spectra are not significantly different from the Smagorinsky-only (Cb=0) simulations. As Cb is increased to Cb=0.4, which is the value recommended by Leith, dissipation and backscatter are significantly over-predicted relative to the DNS, while the net (dissipation minus backscatter) sub-filter dissipation is close to the DNS value. The kinetic energy at the filter wavenumber is in good agreement with the DNS, but this comes at the expense of a deficit of energy at intermediate wavenumbers. The transfer spectrum indicates that Cb=0.4 yields enhanced transfer into wavenumbers near the filter cutoff and reduced transfer into intermediate wavenumbers when compared to smaller Cb. Similar results are found for both stratifications. Overall, this indicates that the Leith model can effectively address the Smagorinsky model's lack of grid-scale backscatter, but does so at the expense of energy at intermediate wavenumbers.