The Stability of Decelerating Shocks Revisited

We present a new method for analyzing the global stability of the Sedov-vonNeumann-Taylor self-similar solutions, describing the asymptotic behavior ofspherical decelerating shock waves, expanding into ideal gas with density\propto r^{-\omega}. Our method allows to overcome the difficulties associatedwith the non-physical divergences of the solutions at the origin. We show thatwhile the growth rates of global modes derived by previous analyses areaccurate in the large wave number (small wavelength) limit, they do notcorrectly describe the small wave number behavior for small values of theadiabatic index \gamma. Our method furthermore allows to analyze the stabilityproperties of the flow at early times, when the flow deviates significantlyfrom the asymptotic self-similar behavior. We find that at this stage theperturbation growth rates are larger than those obtained for unstableasymptotic solutions at similar [\gamma,\omega]. Our results reduce thediscrepancy that exists between theoretical predictions and experimentalresults.Comment: 10 pages, 9 figures. Accepted to ApJ; Expanded discussion of boundary condition