Simple Wave Flows

Abstract

In isentropic flows, simple waves are defined by the condition that the fluid velocity, the local speed of sound and the magnetic field are constant along any curve of one family of characteristics. As a consequence, this family of characteristics is rectilinear. For non-isentropic flows, the same condition cannot be assumed for the entropy. This is due to the fact that the entropy is constant along a streamline. In addition, if the entropy is constant along a family of characteristics, which is distinct from the streamlines, then the flow is isentropic. It might be assumed that a possible solution would be to assume that the entropy is not constant along a simple wave, but that the fluid velocity, local sound speed and magnetic field are constant along a simple wave. But from the characteristic form of the basic equations, viz., Eqs. (1.2.4)–(1.2.10), it is seen that such an assumption is not possible, so that simple waves (in the above sense) do not exist in non-isentropic flow. However, non-isentropic perturbations of simple waves have been shown to exist [30].