The reflexion of a shock wave at a rigid wall in the presence of a boundary layer

Abstract

The paper discusses the reflexion of a shock wave off a rigid wall in the presence of a boundary layer. The basic idea is to treat the problem not as a reflexion but as a refraction process. The structure of the wave system is deduced by a simple mapping procedure. It is found that a Mach stem is always present and that the bottom of this wave is bifurcated—called a lambda foot. The reflexion is said to be regular if the Mach stem and the lambda foot are confined to the boundary layer and irregular if either extends into the main stream. Two types of regular reflexion are found, one that has reflected compression waves and the other that has both reflected compression and expansion waves. Initial conditions are given that enable one to decide which type will appear. There are also two types of irregular reflexion, one that has a Mach stem present in the main stream and the other that is characterized by a four-wave confluence. Finally there are also two processes by which regular reflexions become irregular. One is due to the formation of a downstream shock wave that subsequently sweeps upstream to establish the irregular system and the other is due to boundary-layer separation which forces the lambda foot into the main stream.