Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer–Meshkov instabilities with all density ratios

Abstract

Interfacial fluid mixing driven by an external acceleration or a shock wave are common phenomena known as Rayleigh–Taylor instability and Richtmyer–Meshkov instability, respectively. The most significant feature of these instabilities is the penetrations of heavy (light) fluid into light (heavy) fluid known as spikes (bubbles). The study of the growth rate of these fingers is a classical problem in fundamental science and has important applications. Research on this topic has been very active over the past half-century. In contrast to the well-known phenomena that spikes and bubbles can have quantitatively, even qualitatively, different behaviours, we report a surprising result for fingers in a two-dimensional system: in terms of scaled dimensionless variables, all spikes and bubbles at any density ratio closely follow a universal curve, up through a pre-asymptotic stage. Such universality holds not only among bubbles and among spikes of different density ratios, but also between bubbles and spikes of different density ratios. The data from numerical simulations show good agreement with our theoretical predictions.