Quantitative theory for spikes and bubbles in the Richtmyer−Meshkov instability at arbitrary density ratios in three dimensions

Abstract

It is known that conducting numerical simulations and experiments for the shock-induced Richtmyer–Meshkov instability in three dimensions is much more difficult and time-consuming than that in two dimensions. Therefore, theories can play a more important role in the study of three-dimensional Richtmyer–Meshkov instability. We present analytical formulas for predicting the behavior of growth rate and amplitude of fingers at the unstable Richtmyer–Meshkov interface. Our theory is for both spikes and bubbles, for the arbitrary density ratio between the two fluids, and for the entire development process from early to late times.