How Prandtl number affects the scale-dependent distribution of turbulent kinetic and potential energy in stably stratified turbulence*

Recent direct numerical simulation (DNS) results have revealed striking effects of Prandtl number (Pr) on the dynamics of stably stratified turbulence (Riley, Couchman and de Bruyn Kops, Journal of Turbulence 2023), which are of great importance for understanding flows where Pr>>1. The theoretical study of Bragg and de Bruyn Kops (2024) revealed the mechanism that causes the turbulent kinetic energy (TKE) and turbulent potential energy (TPE) dissipation rates in such flows to be much more strongly dependent on Pr than in flows where the density field is passive. However, the mechanisms underlying the Pr-dependence of the TKE and TPE fields across the full range of scales in the flow are not well understood. To address this, we use an anisotropic filtering approach to analyze the mechanisms governing the TKE and TPE across scales. We use data from massive-scale DNS that explore the effect of Pr for flows with different buoyancy Reynolds numbers and Froude numbers. The analysis reveals how the mechanism presented in Bragg and de Bruyn Kops (2024) can be extended to different scales in the flow, providing insight into the mechanism responsible for the reversal of the buoyancy flux below a certain scale.