OVERTURNING OF NONLINEAR ACOUSTIC-WAVES .2. RELAXING GAS-DYNAMICS

We consider finite-amplitude acoustic disturbances propagating through media in which relaxation mechanisms, such as those associated with t he vibration of polyatomic molecules, are significant. While the effec t of these relaxation modes is to inhibit the wave steepening associat ed with nonlinearity, whether a particular mode is sufficient to preve nt the occurrence of multi-valued solutions will depend on the form of the disturbance and on the characteristic parameters of the relaxatio n. Analysis of this condition is necessary in order to reveal which ph ysical mechanisms actually determine the evolution of the wave profile . This then dictates the scaling of any embedded shock regions. Suffic ient conditions for the occurrence of multi-valued solutions are obtai ned analytically for periodic waves, hence proving that in certain cir cumstances relaxation is in fact insufficient in fully describing the wave propagation. A much more precise criterion is then obtained numer ically. This uses the techniques described in Part 1 for analysing the phenomenon of wave overturning using intrinsic coordinates. Illustrat ions are provided of the development of a harmonic signal for differen t classes of material parameters.