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Budgets of turbulent kinetic energy (TKE) and turbulent potential energy(TPE) at different scales $\ell$ in sheared, stably stratified turbulence areanalyzed using a filtering approach. Competing effects in the flow areconsidered, along with the physical mechanisms governing the energy fluxesbetween scales, and the budgets are used to analyze data from direct numericalsimulation (DNS) at buoyancy Reynolds number $Re_b=O(100)$. The mean TKEexceeds TPE by an order of magnitude at the large scales, with the differencereducing as $\ell$ is decreased. At larger scales, buoyancy is never observedto be positive, with buoyancy always converting TKE to TPE. As $\ell$ isdecreased, the probability of locally convecting regions increases, though itremains small at scales down to the Ozmidov scale. The TKE and TPE fluxesbetween scales are both downscale on average and their instantaneous values arepositively correlated, but not strongly so, and this occurs due to thedifferent physical mechanisms that govern these fluxes. Moreover, thecontribution to these fluxes arising from the sub-grid fields are shown to besignificant, in addition to the filtered scale contributions associated withthe processes of strain-self amplification, vortex stretching, and densitygradient amplification. Probability density functions (PDFs) of the $Q,R$invariants of the filtered velocity gradient are considered. Unlike isotropicturbulence, as $\ell$ increases the sheared-drop shape of the PDF disappearsand the PDF becomes symmetric about $R=0$, meaning regions of vortex stretchingand compression become equi-probable, as well as regions of strainamplification or suppression.

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