The diffraction of a rarefaction wave by a corner

Abstract

An investigation is made of the effect of a small disturbance on the flow in a complete rarefaction wave, for example, the flow produced by the rupture of a membrane originally separating a compressible gas from a vacuum. The perturbation arises from a rigid boundary slightly inclined to the direction of flow. The growth of the perturbed region is studied and the pressure field is calculated for diatomic gases.The nature of the expanding boundary of the perturbed region is investigated. Arguments are put forward which suggest that this boundary can be a weak shock in certain circumstances. A second shock may also appear in some cases, following the first and of greater strength.In an appendix the solutions are extended to monatomic gases and to fluids with an adiabatic index of 2. The latter results are suitable for a comparison with hydraulic experiments.