Shock wave stability in steep density gradients

The stability of spherical accelerating shock waves is discussed via the ex amination of the stability of the new Waxman-Shvarts self-similar solutions to the strong explosion problem with a density profile rho proportional to r(-infinity) with omega > 3. We show that accelerating shock waves that di verge in finite time (obtained for omega larger than a critical value omega (c): omega > omega(c)) are unstable for small and intermediate wavenumbers, in accordance with the conclusions of Chevalier, who studied the stability of planar shock wave propagating in an exponentially decaying density prof ile. However, accelerating shock waves that diverge in infinite time (obtai ned for omega < omega(c)) are stable for most wavenumbers. We find that per turbation of small wavenumber grow or decay monotonically in time, while pe rturbations of intermediate and high wavenumber oscillate in time.