The role of vorticity in shock propagation through inhomogeneous media

A 2-D numerical investigation is undertaken of shock wave propagation into a gas with a nonuniform ("V"-shaped) density profile. This geometry results in the steady infusion of vorticity into the gas behind the shock. The generated vorticity is partially contained between the shock and the analogue to the expected lagging contact surface. Comparison to the results of the 1-D case, achieved by averaging over the inhomogeneous medium, shows that the shock in the 2-D case is faster, and has a smaller jump across it in both pressure and density. A density discontinuity analogous to the 1-D contact surface moves slower than in the 1-D case. In fact, it is no longer a true contact surface, in that there is a small pressure rise across it due to the presence of a vortex sheath. The development of a stationary profile immediately behind the shock is also observed. It is emphasized that using a 1-D model to analyse a shock moving through an inhomogeneous medium will, in general, yield erroneous results for both the shock speed and the parameter jumps across the shock. 2-D vortex dynamics provide a key to understanding the observed shock modifications.