The effect of the overtaking disturbance on a shock wave moving in a non-uniform medium

Abstract

When a shock moves in a non-uniform medium, its motion is influenced both by the non-uniformity ahead of the shock and also by a wave which overtakes the shock. In this paper the overtaking wave is examined in an analytic manner by considering its formation and subsequent propagation. This analysis is then combined with the known ‘freely propagating’ description of the shock motion, in which the overtaking wave is ignored, and results in a description of the shock motion in integral form. For the particular problem of a strong shock propagating in a medium with a power-law density variation, the freely propagating shock law has previously been compared with the available similarity solution. The estimate of the effect of the overtaking wave presented in this paper is shown to provide a significant improvement to the description of the shock motion in this instance.