Shock-driven hydrodynamic instability of a sinusoidally perturbed, high-Atwood number, oblique interface

A shock incident on an interface will cause any initial perturbations on that interface to grow. When the shock front is parallel to the interface, the perturbations grow due to the Richtmyer-Meshkov (RM) process. When there is some tilt between the shock front and the interface, shear flow will result across the postshock interface. Recent experiments on the OMEGA EP laser have studied the hydrodynamic instability growth which results from a supported shock interacting with a sinusoidally perturbed, oblique interface. The observed instability growth was dominated by Richtmyer-Meshkov at early times but became Kelvin-Helmholtz (KH)-like at late times. Previously, this instability growth was described using an analytic model for the deposition of baroclinic vorticity on the interface by a shock combined with a discrete vortex model. Here, we utilize the same baroclinic vorticity deposition model in conjunction with a desingularized, periodic Birkhoff-Rott equation to model instability evolution. The Birkhoff-Rott equation takes into account the vorticity distribution along the interface, whereas the discrete vortex model assumed that all vorticity over each wavelength of the perturbation is confined to a point. We compare the new model to xRAGE simulations and experiments. The model is found to overpredict both the instability growth and shear across the interface by about a factor of two, but correctly predicts that the growth is RM-like at early times and KH-like at late times.