Nonlinear Breaking of Wave Fronts in a Vibrationally Relaxing Gas

Using the method of characteristics, some explicit criteria for the nonlinear breaking of wave fronts in a plane, cylindrically or spherically symmetric flows of a vibrationally relaxing gas are obtained. It is shown that except a spherically converging compressive wave, all compressive waves break only when the initial discontinuity at the wave-head exceeds a critical value, and the effects of vibrational relaxation and that of the wave front curvature are to increase the time of their breaking. It is found that the stabilizing influences of vibrational relaxation and that of the wave front curvature are not strong enough to overcome the breaking tendency of a spherically converging compressive wave; in fact, in contrast to a cylindrically converging wave, it always breaks down before the formation of a focus, no matter how small be the initial discontinuity at the wave-head.