Evolution of Discontinuity at a Disturbance Wave Head in a Radiating Gas
Introduction A NUMBER of problems relating to wave propagation through ideal fluids or fluids with internal relaxation, which are in a constant state at rest before the arrival of the wave front, have been considered previously (a short account is given by Becker and Clarke and McChesney). But much less interest has been shown in the propagation of waves through nonuniform atmospheres, the exceptions being the work of Srinivasan and Vincenti and Clarke.' The present Note applies the theory of characteristics to study the behavior of plane, cylindrical, or spherical wave heads propagating through a spatially uniform but timevarying flow of a radiating gas near the optically thin limit. Exact predictions of the true nonlinear progress of the flow variable gradients at the wave head are made and an expression for the time taken to shock formation is obtained; in addition, the effect of initial wave-front curvature on the growth and decay behavior of nonplanar waves is also discussed. The equations which describe the one-dimensional planar (/ = 0), cylindrically (/=!), or spherically (j = 2) symmetrical motion of a radiating gas near the optically thin limit can be written in the familiar form (see Penner and Olfe, pp. 296, 297, and 385)