Impulsive model for the Richtmyer-Meshkov instability

Abstract

A general formula for the growth rate of the Richtmyer-Meshkov instability [R. D. Richtmyer, Commun. Pure Appl. Math. 13, 297 (1960); E. E. Meshkov, Sov. Fluid Dyn. 4, 101 (1969)] is derived within the framework of the impulsive model. It allows us to predict the growth rate in both heavy-light and light-heavy configurations. This formula is validated over more than 100 cases with various values of the shock strength and the adiabatic exponents. The range of validity of the impulsive model is also specified. Comparisons are performed against the results available in the literature. This expression may be reduced to the Richtmyer or the Meyer-Blewett [Phys. Fluids 15, 753 (1972)] formulas in particular cases. Specific configurations are built in order to emphasize the differences between the latter prescriptions and the formula proposed in this paper.