PROPAGATION AND INTERACTION OF WAVES IN A RELAXING GAS

Propagation of disturbances through a uniform region of a relaxing gas in a duct with spatially varying cross section is analysed using the methods of relatively undistorted waves and weakly nonlinear geometric al optics. Particular attention is focused on situations when the dist urbance amplitude is finite, arbitrarily small and not so small. In ce rtain situations a complete history of the evolutionary behaviour of w aves including weak shocks can be traced out. The asymptotic decay law s for weak shocks in a non-relaxing gas are exactly recovered. The dam ping effects of relaxation and non-planar wavefront configurations on the distortion, attenuation and shock formation of pulses, as they pro pagate, are described in detail. In the small-amplitude high-frequency limit, a solution up to the second order is obtained and numerical co mputations are carried out for typical values of the physical paramete rs involved in the solution. Transport equations are derived for signa ls having all possible wave modes which are mutually coupled and inter act resonantly among themselves. The progressive wave approach describ es the far field behaviour which is governed by the generalized Burger 's equation.