ON THE STABILITY OF DECELERATING SHOCKS

Abstract

Previous work has shown that when the high-density region behind a decelerating pressure-driven shock wave is sufficiently thin, the shock wave is subject to a rippling instability. An analytic analysis of this instability is given here for a decelerating isothermal shock wave, including terms that suppress the instability at short wavelengths. The short-wavelength linear perturbations of the postshock gas are analyzed assuming isothermality. Effects which are important at longer wavelengths are included by analogy with the thin shell case. Results are derived for the maximum growth rate and the minimum unstable wavelength. Exact solutions to these equations are found for the case of a self-similar shock wave in a uniform medium. In particular, the results of the analysis are compared to the exact solutions for the Sedov solution and the wind-driven shock wave.