Over-reflection and instability of shock waves in an inhomogeneous medium

Abstract

Abstract We present a resonant description of hydrodynamic instabilities of shock waves in inhomogeneous media. This approach (1) allows us to clarify the physical mechanisms of instabilities; (2) provides a natural classification of all hydrodynamic instabilities; (3) allows us to simplify the search and prediction of instabilities, reducing the analysis to studying the coefficients of transformation (reflection) of perturbations at the shock front. We apply the developed formalism to the analysis of the resonance characteristics of a model of an accelerating shock wave in an exponential atmosphere and a model of a galactic shock wave. Analysis shows that instability in these models is caused by the effect of spontaneous emission of waves by the shock front while the true resonant effects are insignificant. Finally, we predict that the standing shock wave in an accretion flow on to a point mass must be unstable for the same reasons.