Stationary structures in acoustically active nonequilibrium media with one relaxation process

Abstract

Chemical active mixtures with irreversible reactions, vibrationally excited gases, and nonisothermal plasmas are examples of acoustically active nonequilibrium media. In such media it is possible the existence of stationary nonlinear structures that are different from the step‐wise shock wave structures. In the first part of the present paper it is investigated the solutions of a general acoustical equation, describing in the second order perturbation theory a nonlinear evolution of wide spectrum acoustical disturbances in nonequilibrium media with one relaxation process. Its low‐ and high‐ frequency limits correspond to Kuramoto‐Sivashinsky equation and the Burgers equation with a source, respectively. Stationary structures of general equation, the conditions of their establishment and all their parameters are found analytically and numerically. In acoustically active media it is predicted the existence of the stationary solitary pulse. Then, we consider 1‐D relaxing gas dynamics system of equations with simple Landau‐Teller model of relaxation. The possible stationary profiles are shown in nonequilibrium degree‐ stationary wave speed bifurcation diagram. The boundaries of this diagram are obtained in analytical forms. The field of weak shock wave instability is shown in this bifurcation diagram. Unstable shock wave disintegrates into the sequence of solitary pulses described by the general acoustical equation.