Chian Yeh Goh | Searcharxiv

arXiv2026

A theoretical one-dimensional model for variable-density Rayleigh-Taylor turbulence

In an early theoretical work published in 1965, Belen'kii & Fradkin proposed a turbulent diffusivity model for Rayleigh--Taylor (RT) mixing. We review its derivation and present alternative arguments leading to the same final similarity equation. The original work then introduced an approximation that led to a simplified ordinary differential equation (ODE), which was used primarily to derive the important scaling result, $h \sim (\ln R)gt^2$. Here, we extend the analysis by examining the solutions to both the full similarity ODE and the simplified ODE in detail. It is shown that the full similarity equation captures many now well-known features of non-Boussinesq RT flows, including asymmetric spike and bubble growth and a systematic shift of velocity statistics toward the light-fluid side. Comparisons of the theoretical model with numerical and experimental studies show reasonable agreement in both spatial profiles and growth trends of mixing layer heights. We further show that a global mass correction applied to the simplified solution closely approximates the full solution, highlighting that, to leading order, RT mixing is governed by the competing dynamics between diffusion of $\ln \barρ$ and mass conservation.

physics.flu-dyn↗

arXiv2025

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

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.

physics.flu-dyn↗