Deterministic and stochastic properties of self-similar Rayleigh-Taylor mixing induced by space-varying acceleration

TL;DR

This paper investigates the properties of self-similar Rayleigh-Taylor mixing induced by space-varying acceleration, using group theory and stochastic modeling to understand deterministic and statistical behaviors across different regimes.

Contribution

It introduces a novel analysis of Rayleigh-Taylor mixing with variable acceleration, identifying critical exponents and invariant quantities that distinguish different mixing types.

Findings

Self-similar mixing can be Rayleigh-Taylor or Richtmyer-Meshkov type depending on acceleration exponent.

A critical exponent separates the two mixing regimes.

Invariant quantities characterize the different types of mixing.

Abstract

Rayleigh-Taylor interfacial mixing has critical importance in a broad range of processes in nature and technology. In most instances Rayleigh-Taylor dynamics is induced by variable acceleration, whereas the bulk of existing studies is focused on the cases of constant and impulsive accelerations referred respectively as classical Rayleigh-Taylor and classical Richtmyer-Meshkov dynamics. In this work we consider Rayleigh-Taylor mixing induced by variable acceleration with power-law dependence on the spatial coordinate in the acceleration direction. We apply group theory and momentum model to find deterministic asymptotic solutions for self-similar RT mixing. We further augment momentum model with a stochastic process to study numerically the effect of fluctuations on statistical properties of self-similar mixing in a broad parameter regime. We reveal that self-similar mixing can be Rayleigh-Taylor-type and Richtmyer-Meshkov type depending on the acceleration exponent. We further find the value of critical exponent separating Rayleigh-Taylor-type mixing and Richtmyer-Meshkov-type mixing, and identify invariant quantities characterizing Rayleigh-Taylor-type mixing and Richtmyer-Meshkov-type mixing.