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

Arun Pandian, Snezhana Abarzhi

Research output: Contribution to specialist publicationArticle

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.
Original languageEnglish
Specialist publicationarXiv preprint
Publication statusPublished - 2019

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exponents
momentum
group theory
stochastic processes

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title = "Deterministic and stochastic properties of self-similar Rayleigh-Taylor mixing induced by space-varying acceleration",
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.",
author = "Arun Pandian and Snezhana Abarzhi",
year = "2019",
language = "English",
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AB - 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.

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