Scaling Interface Length Increase Rates in Richtmyer–Meshkov Instabilities

Abstract

The interface area increase produced by largeamplitude wave refraction through an interface that separates fluids with different densities can have important physiochemical consequences, such as a fuel consumption rate increase in the case of a shock–flame interaction. Using the results of numerical simulations along with a scaling analysis, a unified scaling law of the interface length increase was developed applicable to shock and expansion wave refractions and both types of interface orientation with the respect to the incoming wave. To avoid a common difficulty in interface length quantification in the numerical tests, a sinusoidally perturbed interface was generated using gases with different temperatures. It was found that the rate of interface increase correlates almost linearly with the circulation deposited at the interface. When combined with earlier developed models of circulation deposition in Richtmyer–Meshkov instability, the obtained scaling law predicts dependence of interface dynamics on the basic problem parameters.