Small amplitude theory of Richtmyer–Meshkov instability

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Abstract
This paper presents a new analysis of small amplitude Richtmyer–Meshkov instability. The linear theory for the case of reflected rarefaction waves, a problem not treated in previous work, is formulated and numerically solved. This paper also carries out a systematic comparison of Richtmyer’s impulsive model to the small amplitude theory, which has identified domains of agreement as well as disagreement between the two. This comparison includes both the reflected shock and reflected rarefaction cases. Additional key results include the formulation of criteria determining the reflected wave type in terms of preshocked quantities, identification of parameter regimes corresponding to total transmission of the incident wave, discussion of an instability associated with a rarefaction wave, investigation of phase inversions and the related phenomenon of freeze‐out, and study of the sensitivity of the numerical solutions to initial conditions.