The Propagation of a Nonuniform Magnetohydrodynamic Shock Wave Into a Moving Monatomic Fluid

Abstract

Summary An initially uniform magnetohydrodynamic shock wave of arbitrary strength propagates through a channel which consists of two portions of which one has uniform cross-sectional area while the other is of varying cross-sectional area. It is assumed that the flow in the nonuniform section in front of the shock is initially a uniform state and no perturbations (due to the area variations) of this flow reach the shock until the area variation is encountered. When the shock enters the nonuniform section, it is perturbed, the shock strength altered and the subsequent flow is nonisentropic. In addition to the perturbation due to the effect of the area variations on the initially uniform upstream flow, there are two further contributions—viz., a permanent perturbation caused directly b}^ the area changes and a transient disturbance— which propagates with true sonic speed with respect to the flow behind the shock, due to reflections of the permanent perturba­ tion at the shock. Expressions for these various contributions are obtained. The results presented include as special cases propaga­ tion of a nonuniform conventional gas dynamic shock into a moving nonconducting fluid and propagation of a nonuniform hydromagnetic shock wave into a stationary fluid.