Effect of diffuse initial conditions on the Richtmyer–Meshkov instability

Abstract

In this study, we investigate the role of a diffuse interface on the Richtmyer–Meshkov (RM) instability by performing two-dimensional simulations of a single-mode perturbation (wavelength \(\lambda \)) imposed on a diffuse interface (thickness \(\delta \)) between air and \(\hbox {SF}_6\). By varying the ratio \(0.1\le \delta /\lambda \le 0.5\), we examine the effect of the interfacial diffusion thickness on the baroclinic vorticity, perturbation growth, and fluid entrainment. The initial circulation is conserved with respect to \(\delta \), causing a reduction of the initial vorticity magnitude, thus resulting in a reduction of perturbation growth. In the linear regime, the diffusion layer delays perturbation growth, but in the nonlinear regime, the growth becomes insensitive to the initial diffusion thickness, as shown by our power-law scaling accounting for the redistribution of vorticity along the interface. The initial diffusion thickness increases the overall volume of the roll-up, but decreases its surface area. Introducing a new metric (the inter-fluid distance, d) reveals that initially thicker interfaces increase material separation and reduce strain rates within the roll-up structures, resulting in longer diffusion length scales. These structures undergo a gradual thinning over time, causing the inter-fluid distance to decrease to scales comparable to the strain-dominated diffusion length. Therefore, while the strain rate dominates the vortex-core evolution early on, the effect of diffusion may become important at later times, with this transition delayed for thicker initial interfaces.