Prandtl Number Dependence of Stratified Turbulence

Stratified turbulence is affected by buoyancy forces that suppress vertical motion, resulting in horizontal layers of quasi-two-dimensional vortices. The Prandtl number $Pr$ (or Schmidt number) quantifies the relative strengths of viscosity and buoyancy diffusivity which damp small-scale fluctuations at different microscales. Direct numerical simulations (DNS) must resolve the smallest features, requiring high resolution for large $Pr$ (e.g. $Pr=7$ in heat-stratified water and 700 in salt-stratified water). To reduce this computational demand $Pr=1$ is often assumed, possibly introducing discrepancies between DNS and real geophysical flows. In this work, DNS of homogeneous forced stratified turbulence with $Pr=$ 0.7, 1, 2, 4, and 8 are performed for varying stratification strength. Energy spectra, buoyancy flux spectra, spectral energy flux, and physical space fields are compared for scale-specific $Pr$-sensitivity. Intermediate and large scale $Pr$-dependence was found in addition to expected small-scale sensitivity. Based on our results, the $Pr=1$ assumption is not realistic for DNS of $Pr>1$ stratified turbulence: the effects at intermediate, and in some cases, large horizontal scales must be considered, though the computational demand can be prohibitive.