On the breakdown of acceleration waves in a vibrationally relaxing gas

The technique of Jeffrey and Taniuti (1964) is adapted for application to the study of wave front behavior in a general vibrationally relaxing gas model. Consideration of the behavior of converging waves establishes that a cylindrical compressive wave breaks down only if the initial wave amplitude equals or exceeds a critical value, while a spherical compressive wave always breaks before the formation of a focus, irrespective of how small the initial wave amplitude may be. It is observed that, in an expanding motion, the effect of wave front curvature is to increase the time of breaking; in a converging gas, its effect is to increase the time of breaking.