Wave propagation at high dissociation temperatures

Waves in ideal dissociating gases are examined in the limit of large dissociation temperatures. Both strong shock waves and weak finite-amplitude signalling problems are considered. The shock analysis is based on the Freeman limit, and an extension to higher Mach numbers is given. Even small-amplitude near-field theories, which are concerned with times comparable to the signal scale, can contain nonlinear exponential terms when the dissociation temperature is large. A corresponding endothermic Clarke equation is derived and solutions are determined in the Newtonian limit. Far-field theory, involving both convective and chemical nonlinearities, is also discussed. Suitable high-frequency solutions are obtained, together with results for the evolution of the shock path and the decay of the signal amplitude.