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

The dynamics of turbulent Rayleigh–Taylor (RT) mixing layers is investigated across a broad range of Atwood and Reynolds numbers using the statistically stationary RT flow configuration – a computational framework that enables simulation of a minimal flow unit for RT flows at reduced cost. 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 $\rho _H$ and $\rho _L$ . Most normalized quantities collapse well across the parameter space. In some cases, variations in the Atwood number $A$ (or 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, $\alpha =\dot {h}^2/4Agh$ , 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 (1965 Trudy FIAN 29, 207–238). Applying this $A^*$ scaling to existing RT data, the corresponding growth parameter, $\alpha ^*=\dot {h}^2/4A^*gh$ , remains nearly constant across all Atwood numbers considered, offering a unified scaling for variable-density RT flows.