Behaviour of a discontinuity at the wave-head propagating through a relaxing gas

The rate of amplification of a discontinuity at the wavefront moving through a nonuniform atmosphere of a relaxing gas is discussed theoretically. Weak and strong equilibrium states are considered, and the medium before the wave is assumed to be spatially uniform and time dependent. Basic equations for the one-dimensional unsteady motion of a relaxing gas are defined in terms of a continuity equation. Characteristic forms are developed with parameters for the distance into the gas and the time factor and the evolution of the discontinuity at the wavefront is examined. Propagation of diverging, converging, and spherical waves in a uniform medium are analyzed, along with a short time period of evolution into a nonuniform medium evolving over time. A weak equilibrium state is found to possibly aid in the development of a shock, while a strong equilibrium state always impedes the formation of a shock at the wavefront.