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

Abstract

Interfacial fluid mixing driven by an external force or a shock wave is a common phenomenon known as Rayleigh-Taylor instability or Richtmyer-Meshkov instability, respectively. The most significant features of these instabilities are the penetrations of heavy fluid into light fluid, which are known as spikes; and the penetrations of light fluid into heavy fluid, which are known as bubbles. The study of the growth rates of spikes and bubbles is a classical problem in fundamental science and has important applications. The research on this topic is very active over the past half-century. In contrast to the well-known phenomena that spikes and bubbles can have quantitatively, even qualitatively, different behaviors, we report a surprising result: in terms of scaled dimensionless variables, all spikes and bubbles at any density ratio closely follow a universal curve, up to 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. In addition, such scaling is applicable to both planer systems and cylindrical systems. The discovery of this property is not only of merit to the theoretical modeling in Rayleigh-Taylor and Richtmyer-Meshkov instabilities, but also useful for numerical simulations and experiment research. The data from numerical simulations and experiments show good agreement with our theoretical predictions.

Date of Award	15 Jul 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Qiang ZHANG (Supervisor)