On the Propagation of Weak Discontinuities Along Bicharacteristics in a Radiating Gas

Abstract

The propagation of weak discontinuities along bicharacteristic curves in the characteristic manifold of the differential equations governing the flow of a radiating gas near the optically thin limit has been discussed. Some explicit criteria for the growth and decay of weak discontinuities along bicharacteristics are given. As a special case, when the discontinuity surface is adjacent to a region of uniform flow, the solution for the velocity gradient at the wave head is specialized to the plane, cylindrical, and spherical waves. For expandng waves, the attenuation induced by geometric factors and the radiative flux, and the growth induced by the upstream flow Mach number are discussed. It is shown that a compressive disturbance steepens into a shock only if the initial disturbance is sufficiently strong.