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Recently, direct numerical simulations (DNS) of stably stratified turbulencehave shown that as the Prandtl number ($Pr$) is increased from 1 to 7, the meanturbulent potential energy dissipation rate (TPE-DR) drops dramatically, whilethe mean turbulent kinetic energy dissipation rate (TKE-DR) increasessignificantly. Through an analysis of the equations governing the fluctuatingvelocity and density gradients we provide a mechanistic explanation for thissurprising behavior and test the predictions using DNS. We show that the meandensity gradient gives rise to a mechanism that opposes the production offluctuating density gradients, and this is connected to the emergence oframp-cliffs. The same term appears in the velocity gradient equation but withthe opposite sign, and is the contribution from buoyancy. This term isultimately the reason why the TPE-DR reduces while the TKE-DR increases withincreasing $Pr$. Our analysis also predicts that the effects of buoyancy on thesmallest scales of the flow become stronger as $Pr$ is increased, and this isconfirmed by our DNS data. A consequence of this is that the standard buoyancyReynolds number does not correctly estimate the impact of buoyancy at thesmallest scales when $Pr$ deviates from 1, and we derive a suitable alternativeparameter. Finally, an analysis of the filtered gradient equations reveals thatthe mean density gradient term changes sign at sufficiently large scales, suchthat buoyancy acts as a source for velocity gradients at small scales, but as asink at large scales.

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics