Linear interaction analysis for Richtmyer-Meshkov instability at low Atwood numbers

Abstract

A recent formulation [J. Griffond, Phys. Fluids17, 086101 (2005)] of the linear interaction analysis (LIA) for mixtures of two perfect gases is applied to a field including a sinusoidal diffuse interface between two perfect gases. It offers an original way to investigate the initial phase of the Richtmyer-Meshkov instability. The approach is valid only in the limit of gases with close molar mass and specific heat (low Atwood numbers), but it applies to interfaces of arbitrary corrugation amplitude and diffusion thickness without Mach number limitation on the shock wave. The vorticity field deduced from LIA compares favorably with two-dimensional numerical simulations. In their limit of common validity, the LIA and the formulas of Wouchuk [Phys. Rev. E63, 056303 (2001); Phys. Fluids 8, 2890 (2001)] predict close asymptotic growth rates, contrary to impulsive models. The correction for initial diffusion of the interface proposed by Brouillette and Sturtevant [J. Fluid Mech.263, 271 (1994)] shows only weak discrepancies with the present results.