ANALYTIC THEORY OF RICHTMYER-MESHKOV INSTABILITY FOR THE CASE OF REFLECTED RAREFACTION WAVE

An analytic theory of the Richtmyer-Meshkov (RM) instability for the c ase of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a ''stand-alone'' rarefa ction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement w ith earlier linear and nonlinear numerical results. Applicability of t he prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initi al conditions of the unperturbed Riemann problem, identically zero den sity difference across the contact interface both before and after int eraction, and zero normal acceleration of the interface. This confirms that the RM instability is not caused by the instant normal accelerat ion of the interface, and hence, is not a type of Rayleigh-Taylor inst ability. The RM instability is related to the growth of initial transv erse velocity perturbations at the interface, which may be either pres ent initially as in symmetrical Riemann problem, or be induced by a sh ock passing a corrugated interface. (C) 1996 American Institute of Phy sics.