A note on the pseudo-stationary flow behind a strong shock diffracted or reflected at a corner

Abstract

It is shown that the equations of an unsteady compressible flow in the ( x, y )-plane, which is expressible in terms of the two variables x/t and y/t only, can be reduced to those of a steady compressible flow with a non-conservative field of external forces and a field of sinks. The steady-flow problems of this type, which correspond to the diffraction or reflexion of a plane shock travelling parallel to a rigid wall and reaching a corner, are discussed qualitatively. It is shown that, under certain conditions, there are regions in the corresponding steady flows which are entirely supersonic and for which a simple solution can be given without determining the whole field of flow. No complete solution for the whole field of flow has yet been given. In the diffraction, at a convex corner, of certain strong shocks, it is shown that there can be an area of Prandtl-Meyer flow, uniformly increasing with time, and that the upper limit to which it can extend is calculable as a characteristic curve in the corresponding steady flow. In the case of regular reflexion beyond a concave comer, or reflexion at a concave corner which gives rise to a reflected shock passing through the corner, it is shown that there can be areas of uniform flow, uniformly increasing with time, and that the upper limits to which they can extend are arcs of circles, which appear as sonic curves in the corresponding steady flows.