On the fundamentals of Richtmyer-Meshkov dynamics with variable acceleration

TL;DR

This paper investigates Richtmyer-Meshkov instability under variable acceleration using group theory, revealing how initial conditions influence early growth and identifying stable asymptotic solutions for late-time dynamics, with implications for experiments and simulations.

Contribution

It introduces a novel theoretical framework for RMI with variable acceleration, deriving new solutions and stability analysis, advancing understanding beyond classical steady or impulsive cases.

Findings

Early-time growth-rate depends on initial conditions, independent of acceleration parameters.

A family of stable asymptotic solutions describes late-time interface dynamics.

Nonlinear dynamics characterized by wavelength and amplitude, matching observations.

Abstract

Richtmyer-Meshkov instability (RMI) plays important role in nature and technology, from supernovae and fusion to scramjets and nano-fabrication. Canonical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. This work focuses on RMI induced by acceleration with a power-law time-dependence, and applies group theory to solve the classical problem. For early-time dynamics, we find the dependence of RMI growth-rate on the initial conditions and show it is free from 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 the solutions stability. For each of the solutions, the interface dynamics is directly linked to the interfacial shear, and 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 excellent agreement with observations. We elaborate new theory benchmarks for experiments and simulations, and put forward a hypothesis on the role of viscous effects in interfacial nonlinear RMI.