Self-similar scaling of variable-density Rayleigh-Taylor turbulence

Abstract

The dynamics of self-similar Rayleigh-Taylor (RT) mixing layers are investigated across a broad range of Atwood and Reynolds numbers using the statistically stationary Rayleigh-Taylor (SRT) flow configuration - a computational framework that enables simulation of self-similar RT flows at reduced cost compared to conventional temporally growing mixing layers. Normalizations are developed for all dominant non-transport terms in the continuity, mixed mass, and turbulent kinetic energy budgets in terms of the input parameters: the mixing layer height $h$, gravitational acceleration $g$, and fluid densities $ρ_H$ and $ρ_L$. Most normalized quantities collapse well across the parameter space. In some cases, variations in the Atwood number $A$ (or equivalently, the density ratio $R$) lead to consistent integral magnitudes but spatially shifted profiles. These shifts are primarily related to a division by density and are similarly observed in the analytical solution of the one-dimensional variable-density diffusion problem. The analysis introduces a reference density for the mixed mass, examines trends in Favre-averaged statistics, and derives a scaling law for the growth rate of the mixing layer. For height definitions encompassing the full extent of the layer, the conventional growth parameter, $α= \dot{h}^2/4Agh$, varies with Atwood number. Our analysis leads to an alternative formulation using an effective Atwood number, $A^*= (\ln R)/2$, that is consistent with the scaling proposed by Belen'kii & Fradkin (Trudy FIAN, vol. 29, 1965, pp. 207-238). The corresponding growth parameter, $α^*=\dot{h}^2/4A^*gh$, remains nearly constant across all Atwood numbers considered, offering a unified scaling for variable-density RT flows.