Effects of large density contrasts on scale-by-scale energy transfers in Unstably Stratified Homogeneous Turbulence

We investigate numerically the effects of significant density contrasts on the dynamics of buoyancy-driven turbulence commonly encountered in geophysical and astrophysical flows. To this aim, we use the Variable Density equations^1,2, extending the Boussinesq approximation to large Atwood number flows in the low Mach number limit. In particular, we consider the framework of Unstably Stratified Homogeneous Turbulence (USHT)³, a paradigm of Rayleigh-Taylor mixing layers with a constant background vertical density gradient.

The focus is on the scale-by-scale dynamics of eddies4, emphasizing the growth rate of turbulent kinetic energy, the anisotropy of the density structures, and the small-scale mixing.

To address these different topics, highly resolved Direct Numerical Simulations (DNS) of Variable Density and Boussinesq USHT have been performed with the 3D pseudo-spectral code STRATOSPEC^5,6. Scale-by-scale kinetic energy budgets are established and assessed with the DNS data, then critically compared with those analyzed from the Boussinesq framework. The equations comply with the one-point energy budget equations for large scales. More importantly, they reduce to transport equations at very small scales for the mean energy dissipation rate.  Similarity scales are deduced from equations. Early stages of the mixing exhibit energy fluxes from small to large scales, while at later times, a classical energy cascade is established.