Nonlinear and buoyancy pressure correlations in stably stratified turbulence

We analyse direct numerical simulations of homogeneous, forced, stably stratified turbulence to study how the pressure-strain and pressure scrambling terms are modified as stability is increased from near neutral to strongly stratified conditions. We decompose the pressure into nonlinear and buoyancy components, and find that the buoyancy part of the pressure-strain correlation changes sign to promote large-scale anisotropy at strong stability, unlike the nonlinear component, which always promotes large-scale isotropy. The buoyancy component of the pressure scrambling term is positive semidefinite and increases monotonically with stability. As its magnitude becomes greater than the nonlinear component (which is negative), the overall scrambling term generates buoyancy flux at very strong stability. We apply quadrant analysis (in the pressure-gradient space) to these correlations to study how contributions from the four quadrants change with stability. Furthermore, we derive exact relationships for the volume-averaged buoyancy components of these correlations which reveal (i) the buoyancy component of the pressure-strain correlation involves a weighted sum of the vertical buoyancy flux cospectrum, so counter-gradient buoyancy fluxes contribute to enhanced anisotropy by transferring vertical kinetic energy into horizontal kinetic energy; (ii) the buoyancy component of the pressure scrambling term involves a weighted sum of the potential energy spectrum; (iii) the weighting factor accentuates contributions from layered motions, which are a prominent feature of strongly stratified flows. These expressions apply generally to all homogeneous stratified flows independent of forcing and across all stability conditions, explaining why these effects have been observed for both forced and sheared stably stratified turbulence simulations.