Backscatter in stratified turbulence

Kinetic energy exchanges between resolved and sub-grid motions in geophysical turbulence simulations can act in both directions: downscale transfer contributes to dissipation of the resolved kinetic energy, while upscale transfer, known as backscatter, can energize the resolved scales. Backscatter can be significant in real turbulence but is not included in many sub-grid models. This talk will discuss properties and modelling of backscatter in numerical simulations of decaying homogeneous stratified turbulence. In direct numerical simulations (DNS), we measure backscatter by filtering the solution and explicitly calculating the sub-filter energy transfers. In large eddy simulations, we include backscatter following the Leith stochastic backscatter model along with Smagorinsky eddy viscosity. Different values of the Leith coefficient are considered, and the modelled backscatter is compared to that measured in the DNS. Overall, the Leith model is capable of generating realistic levels of backscatter if the Leith coefficient is not too large. Strong backscatter forcing also changes the resolved turbulent energy transfer and leads to a reduction of kinetic energy in the inertial range. Dependence on stratification will also be discussed.