Growth rate of Rayleigh-Taylor turbulent mixing layers with the foliation approach

TL;DR

This paper introduces a new analytical model for Rayleigh-Taylor turbulent mixing layer growth rates, utilizing foliated averages and spectra, to reconcile discrepancies between experiments and simulations.

Contribution

It presents the first analytical expression for growth rates based on foliated spectra, applicable to self-similar Rayleigh-Taylor turbulence with variable acceleration.

Findings

Growth rate depends on acceleration history.

Foliated spectra determine the growth rate's value.

Model aligns with numerical simulations.

Abstract

For years, astrophysicists, plasma fusion and fluid physicists have puzzled over Rayleigh-Taylor turbulent mixing layers. In particular, strong discrepancies in the growth rates have been observed between experiments and numerical simulations. Although two phenomenological mechanisms (mode-coupling and mode-competition) have brought some insight on these differences, convincing theoretical arguments are missing to explain the observed values. In this paper, we provide an analytical expression of the growth rate compatible with both mechanisms and is valide for a self-similar, low Atwood Rayleigh-Taylor turbulent mixing subjected to a constant or time-varying acceleration. The key step in this work is the introduction of {\it foliated} averages and {\it foliated} turbulent spectra highlighted in our three dimensional numerical simulations. We show that the exact value of the Rayleigh-Taylor growth rate not only depends upon the acceleration history but is also bound to the power-law exponent of the {\it foliated} spectra at large scales.