Asymptotic growth in the linear Richtmyer–Meshkov instability

Abstract

An analytic model for the asymptotic growth in the linear Richtmyer–Meshkov instability is presented. Analytic formulae for the interface velocity are obtained both in the weak and the strong shock limits, whether a shock or a rarefaction are reflected. For weak shocks, the irrotational approximation is used. For strong shocks, the vorticity in the bulk must be also taken into account. It is seen that this bulk vorticity actually lowers the velocity predicted by the irrotational approximation. An explicit approximate formula is given in this case. It agrees very well with a previously reported numerical solution. Perturbation freeze-out is also considered in the weak shock limit. It is concluded that this instability is driven by the vorticity left by the shocks at the interface and in the fluids.