Weak shock waves in negative-dispersion nonequilibrium media

The “frozen” and equilibrium shock adiabats for a gas with sustained steady-state nonequilibrium are constructed accurate to the second order of smallness. With these adiabats, the pattern of and stability conditions for weak shock waves in negative-dispersion nonequilibrium media, where the speed of low-frequency (equilibrium) sound exceeds that of high-frequency (frozen) sound, are considered. On the basis of a model nonlinear equation describing the evolution of gasdynamic perturbations in low-dispersion media, the nonstationary evolution of shock waves at a negative low-frequency nonlinearity coefficient is analyzed. This situation corresponds to a low-frequency adiabat convex upwards. It is shown that a step autowave may arise in this case whose amplitude is entirely specified by the nonequilibrium parameters of the medium and correlates with the point where the low-frequency and high-frequency adiabats intersect. In addition, it is found that the initial unsteady shock wave may split into two steady ones: a step autowave followed by a steady smooth-front expansion shock.