Buoyancy-pressure correlations in stably stratified turbulence

A defining aspect of stably stratified turbulence is the damping of vertical velocity fluctuations by the buoyancy force. This increasingly promotes large-scale anisotropy as flow stability increases from near-neutral to very stable conditions. Consequently, both the pressure-strain redistribution mechanism and the vertical buoyancy flux play key roles in how energy is exchanged among the three components of turbulent kinetic energy (TKE) and turbulent potential energy (TPE). Here, we focus specifically on the pressure fluctuations caused by density fluctuations and their correlations with the diagonal components of the rate-of-strain tensor (pressure-strain redistribution) and the density gradients (pressure scrambling). We present closed-form expressions for the (i) buoyancy pressure-strain redistribution (source/sink in both the horizontal and vertical TKE budgets); and (ii) buoyancy pressure scrambling (source/sink in the vertical buoyancy flux budget). These expressions reveal the connections between (i) the buoyancy pressure-strain redistribution and the vertical buoyancy flux and (ii) buoyancy pressure scrambling and density variance. We study these relationships using a dataset of direct numerical simulations (DNS) of forced, stably stratified turbulence. In this dataset, we observe more frequent counter-gradient (CG) buoyancy fluxes as stability is increased, which drive the reduction in the conversion of vertical TKE into TPE. These CG fluxes also promote large-scale anisotropy in the flow through increased conversion of vertical TKE into horizontal TKE by the buoyancy pressure-strain redistribution, which is contrary to the physical concepts underlying return-to-isotropy models.