Energy cascades in Rayleigh-Taylor turbulence.

We analyze the scale-to-scale energy transfer in 2D and 3D compressible Rayleigh-Taylor (RT) turbulence using the coarse-graining approach. Based on the Favre scale decomposition, we outline the energy pathways in RT flows which include transfer between potential energy, kinetic energy at different scales, and internal energy. In particular, two flux terms are responsible for kinetic energy transfer across scales, namely baropycnal work $\Lambda_\ell$, which arises from work done by pressure gradients on the turbulent mass flux, and deformation work $\Pi_\ell$, which is solely due to multi-scale turbulent velocity fields. Within the energy pathways, we can identity a range of scales in which the kinetic energy fluxes $\Lambda_\ell$ and $\Pi_\ell$ are not directly affected by either external inputs at large scales or by dissipation at small scales. We call this range of scales the inertial range in turbulent RT flows over which kinetic energy cascades. We carry out a detailed analysis of energy budgets, including the cascades, as a function of scale using high resolution turbulent RT simulations in 2D and 3D. The paper then characterizes the anisotropic energy cascades and anisotropic spectra of density and velocity in RT flows. Furthermore, the paper discusses similarities and differences between two-species incompressible RT turbulence and our single-species compressible RT turbulence.