Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence*

The budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales in sheared, stably stratified turbulence (SSST) are analyzed using a filtering approach together with data from direct numerical simulations. Fluctuations of the flow about the mean-field state are shown to be strong, and at larger scales, buoyancy is almost never observed to be positive, such that buoyancy always acts to convert TKE to TPE at these scales. As the filter length is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. Recent analytical results are used to investigate the physical mechanisms governing the TKE and TPE fluxes between scales. These TKE and TPE fluxes exhibit large fluctuations about their mean values and are positively correlated, but weakly so, and this is shown to be due to the fact that fundamentally different physical mechanisms govern the two fluxes. Moreover, the contribution to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain-rate self-amplification, vortex stretching, and density gradient amplification by the strain-rate field.