Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries

Abstract

Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We study the flow of an ideal gas with adiabatic index $\gamma$ with initial density $\rho \sim r^{-\omega }$, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space $\gamma ,\omega$, and draw the connections between the different geometries. We find that only type II self-similar solutions are valid in converging shocks, and that in some cases, a converging shock might not create a reflected shock after its convergence. Finally, we derive analytical approximations for the similarity exponent in the entirety of parameter space.

13 pages, 12 figures