A novel class of solutions for the strong spherical shocks driven by expanding pistons

The shocks in this configuration appear in numerous problems of astrophysics and geophysics. Known are self-similar solutions for a piston expanding in a radially stratified medium with a power-law density distribution or for a power-law time-dependence of piston velocity. We show that it is possible to generalize these solutions by exploiting an effect of geometrical stretching of the shocked material in a spherical geometry. For not-too-stiff equation of state, e.g. that of a fully-ionized plasma (gamma=5/3), the flow within the shocked gas turns out to be nearly isobaric. This allows one to produce analytical solutions for radial density variation of an ambient gas of the form of bumps or dimples, and for temporal variations of the piston velocity of the form of bumps or dimples. In particular, it is possible to describe interaction of a supernova-driven shock with the layers of a lower (higher) density or their combinations. Work performed for U.S. DOE by LLNS LLNL under Contract No. DE-AC52-07NA27344.