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Abstract

Abstract. Singular surface theory is used to study the evolutionary behaviour of an unsteady three-dimensional motion of a shock wave of arbitrary strength propagating through a non-ideal gas. The dynamical coupling between the shock front and the induced discontinuities behind it is investigated by considering an infinite system of transport equations governing the strength of a shock wave and the induced discontinuities behind it. This infinite system, when subjected to a truncation approximation, efficiently describes the shock motion. Disturbances propagating on the shock and the onset of shock-shocks are briefly discussed. For a two-dimensional shock motion, our transport equations bear a structural resemblance to those of geometrical shock dynamics. Attention is drawn to the connection between the transport equation obtained by using the truncation rule and the one obtained by using the characteristic rule. The effects of van der Waals' excluded volume and wavefront geometry on the evolutionary behaviour of shocks are discussed. Introduction.The problem of determining the motion of a shock wave of arbitrary strength has received considerable attention in the literature, and it has been a subject of great interest form both mathematical and physical points of view. If the shock is weak enough for the entropy changes across it to be negligible, a number of analytical approximations, such as the simple wave method of Friedrichs and the method of perturbation of characteristics of Lin (see