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

Recent DNS of stably stratified turbulence show that when increasing the Prandtl number ($Pr$) from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity gradients (FVG) and fluctuating density gradients (FDG) we provide a mechanistic explanation for this surprising behavior. We show that the mean density gradient gives rise to a mechanism that opposes the production of FDG and is connected to the emergence of ramp-cliffs. An equal but opposite term appears in the FVG equation, corresponding to the contribution from buoyancy, and this is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$. Our analysis predicts that the effects of buoyancy on the FVG become stronger as $Pr$ is increased, which is confirmed by our DNS data. Due to this, the buoyancy Reynolds number does not correctly estimate the impact of buoyancy on FVG when $Pr eq 1$, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the buoyancy term acts as a source for FVG at small scales, but as a sink at large scales.