A study of the structure of the magnetohydrodynamic switch-on shock in steady plane motion

Abstract

The structure of the steady magnetohydrodynamic switch-on shock wave is investigated for several orderings of the four diffusivities involved in the problem. The various orderings are approximated to by allowing one or more of the appropriate diffusivities to approach zero, and approximate solutions that are uniformly valid to order unity are sought. In general, singular perturbation problems are encountered, the number occurring (from zero to a maximum of three) depending upon the ordering of the diffusivities and the magnitude of the downstream velocity normal to the shock relative to certain critical velocities downstream of the shock. Where necessary, the approximate solutions are rendered uniformly valid to first order by the insertion of boundary layers, for which the approximate equations are determined to first order. For most of the cases considered, the limiting forms of the integral curves are determined and they are sketched in appropriate three-dimensional phase spaces.