On the propagation of shock waves through regions of non-uniform area or flow

This paper refers to the work of Moeckel (1952) on the interaction of an oblique shock wave with a shear layer in steady supersonic flow and the work of Chester (1955) and Chisnell (1957) on the propagation of a shock wave down a non-uniform tube. It is shown that their basic results can be obtained by the application of the following simple rule. The relevant equations of motion are first written in characteristic form. Then the rule is to apply the differential relation which must be satisfied by the flow quantities along a characteristic to the flow quantities just behind the shock wave. Together with the shock relations this rule determines the motion of the shock wave. The accuracy of the results for a wide range of problems and for all shock strengths is truly surprising. The results are exactly the same as were found by the authors cited above. The derivation given here is simpler to perfom (although the original methods were by no means involved) and of somewhat wider application, but the main reason for presenting this discussion is to try to throw further light on these remarkable results. In discussing the underlying reasons for this rule, it is convenient to use the propagation in a non-uniform tube as a typical example, but applications to a number of problems are given later. A list of some of these appears at the beginning of the introductory section.