Structure and stability of a spherical shock wave in a Van der Waals gas

Abstract

Strong spherical shock waves are studied for an imperfect gas, here modelled by a van der Waals equation of state. Similarity solutions of Guderley type are shown to exist, in which the radius of the shock is proportional to (-/)", where t is time measured from the moment at which the shock focuses. The exponent a depends on both the ratio of specific heats, y, and on the van der Waals excluded volume, b. For small b, the solution resembles the Guderley solution and is well described by the Chester-Chisnell-Whitham (CCW) approximation. A new branch of solutions, which the CCW approximation fails to locate, is shown to exist for larger b.