On the behaviour of a weak discontinuity in a radiation-induced flow field

Abstract

The growth and decay behavior of weak gas-dynamic discontinuities has been studied by taking into account the influence of coupling between the time-dependent gas-dynamic field and the radiation field. The thermal radiation effects have been investigated using a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative-heat-transfer equation. It is proved that the time-dependent radiation field, gives rise to a radiation-induced weak wave, which has a negligible influence on the nonrelativistic flow properties of the gas-dynamic field. It is also shown that there is an interesting competition between radiation stresses to resist the steepening tendency of a compressive, weak wave to stabilize itself and the thermal conduction effects to destabilize the wave. It is found that under thermal radiation effects, shock wave formation is either disallowed or delayed. Three cases, diverging waves, converging waves, and plane waves, have been studied separately with reference to the growth and decay behavior of their amplitudes. For converging waves, it is found that either they form a caustic under curvature effects or if it happens to be a compressive wave with the magnitude of its initial amplitude greater than a certain critical value, then it grows into a shock wave within a finite critical time before a caustic can be formed.