Cylindrical and spherical shock waves in monatomic conducting fluids

Summary

A previously derived first order differential relation between shock strength and channel area variations, obtained when an initially uniform magnetohydrodynamic shock wave of arbitrary strength propagates with constant speed into an ideal, perfectly conducting, monatomic compressible fluid at rest, is integrated numerically to give a shock strength-area relation valid for channels with continuous area variation.

Particular area distributions allow a discussion of converging cylindrical and spherical magnetohydrodynamic shocks. It is shown that near the center, the strengths of such shocks are independent of the applied magnetic field and are given by their gas dynamic values.

The usual theory for gas dynamic shock propagation in non-uniform ducts is contained as a special case of the theory presented.