On Richtmyer-Meshkov unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration

TL;DR

This paper investigates the dynamics of Richtmyer-Meshkov instability under time-dependent acceleration, revealing how initial conditions influence early growth and identifying stable asymptotic solutions that characterize nonlinear coherent structures.

Contribution

It introduces a novel analytical approach using group theory to solve RMI with variable acceleration, providing new insights into late-time behavior and stability of interfacial structures.

Findings

Early-time growth-rate depends on initial conditions, not acceleration parameters.

Identifies a family of stable asymptotic solutions with specific interface properties.

Proposes new theoretical benchmarks for experimental and simulation validation.

Abstract

Richtmyer-Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to solve the long-standing problem. For early-time dynamics, we find the dependence of the growth-rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time dynamics, we find a continuous family of regular asymptotic solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and we study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear, the non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that nonlinear coherent dynamics in RMI is characterized by two macroscopic length-scales -- the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined, these being respectively, the Atwood, Taylor, convergence, minimum-shear, and critical bubbles, among others. We also elaborate new theory benchmarks for future experiments and simulations.