A model is presented for the linear growth rate of the Richtmyer–Meshkov instability (RMI) for a reflected shock (RS) and a reflected rarefaction (RR) based on the analytical solution of Fraley Phys. Fluids 29, 376 (1986) for a RS. The model is developed using statistical comparisons with known numerical, analytical, and experimental growth rates over a wide range of hydrodynamic conditions. The Fraley model is found to describe growth rates for a RS very well, except when a strong shock encounters a highly compressible downstream fluid. This is mitigated by introducing a targeted heuristic term that modifies the effect of vorticity in the downstream fluid. The model is then extended to a RR by imposing the theoretical result that rarefactions do not produce vorticity and using an effective velocity representing the central part of the rarefaction in the irrotational solution. The result is a closed-form model for the linear RMI growth rate for a RS and RR that is simple and intuitive with excellent overall accuracy.
Guy Dimonte (Fri,) studied this question.