Toward analytic theory of the Rayleigh-Taylor instability: lessons from a toy model

TL;DR

This paper proposes a universal stochastic wave model to explain the turbulent phase of Rayleigh-Taylor instability, supported by numerical simulations of a new shell model that captures key phenomenological features.

Contribution

It introduces a novel stochastic wave framework for Rayleigh-Taylor turbulence and validates it through extensive shell model simulations.

Findings

The turbulent phase can be modeled as a stochastic wave with constant speed.

The wave connects states related to initial discontinuity and stationary turbulence.

Numerical simulations support the theoretical model.

Abstract

In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary deterministic chaos in a renormalized time, has two constant limiting states at both sides. These states are related to the initial discontinuity at large scales and to stationary turbulence at small scales. The theoretical analysis is confirmed with extensive numerical simulations made for a new shell model, which features basic properties of the phenomenological theory for the Rayleigh-Taylor instability.