Steepening of waves in radiative magnetohydrodynamics

Abstract

Singular surface theory is used to determine the modes of wave propagation and development of discontinuities at planar and cylindrical wave fronts. It is investigated as to how the effects of thermal radiation and magnetic field strength influence the steepening and flattening of wave fronts. Although the effect of magnetic field, whether axial or azimuthal, is to increase the shock formation distance, it, unlike the effect of thermal radiation, cannot offset the tendency of a compression wave-head, carrying a jump discontinuity (no matter how weak initially), to grow into a shock wave after a finite running length. In an optically thick gas with negligible radiation pressure and energy, an increase in the radiative flux reduces the shock formation distance; this is in contrast to the corresponding result for an optically thin gas where an increase in the radiative flux causes shock formation distance to increase. However, numerical calculations show that in a temperature range 9 × 10 4 < T < 2 × 10 5, the combined effect of radiation pressure, energy and flux is to delay the formation of a shock wave. It is found that the decaying of expansion waves is enhanced (slowed down) due to the presence of thermal radiation (magnetic field).