Resolution of an Initial Shear-Flow Discontinuity in One-Dimensional Hydromagnetic Flow.

Abstract

The problem of the resolution of an initial shear-flow discontinuity in an infinitely conducting, compressible fluid is treated. The discussion applies equally well to a flow which is initially parallel to a perfectly conducting wall The basis of both problems is that a shear flow is an "inadmissible" hydromagnetic contact discontinuity if a component of the magnetic field normal to the surface of discontinuity is present. The motion which results when a shear-flow discontinuity is present initially is investigated It is shown that this motion may be described in terms of known solutions of the hydromagnetic shock and continuum equations. The dependence of the final constant state of the medium on the initial state is analyxed by analytical and numerical means. Formulae for various quantities of interest are given for the limiting cases of weak and strong initial shear flows