Linear perturbation growth at a shocked interface

An analytic model for the Richtmyer-Meshkov instability in the linear regime is presented. Approximate formulas for the interface asymptotic velocity are obtained for weak incident shocks. When a rarefaction is reflected, a comparison with recent experiments is shown. The phase reversal is also discussed. The areal mass density perturbations are studied and they are found to grow asymptotically linearly with time. For strong shocks there is a shift due to the entropy disturbances behind the shock(s). The impulsive model is modified to consider the different accelerations exerted by the reflected and transmitted fronts. It agrees with the compressible solution in the weak shock limit.