Rayleigh-Taylor turbulence with singular nonuniform initial conditions

TL;DR

This paper investigates Rayleigh-Taylor turbulence with singular initial conditions, revealing how the mixing layer growth depends on initial singularity and proposing a model that aligns with numerical simulations, connecting to spontaneous stochasticity.

Contribution

It introduces a new understanding of turbulence evolution with singular initial conditions and proposes a closure model matching numerical results.

Findings

Growth depends on initial singularity exponent c

Universality recovered via efficiency metric

Closure model accurately predicts temperature profiles

Abstract

We perform direct numerical simulations of three dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood number; the long-time growth is still self-similar, but not anymore proportional to $t^2$ and depends on the singularity exponent $c$ of the initial profile $\Delta T \propto z^c$. We show that the universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.