Nonlinear Dynamics of Acoustic Instability in a Vibrationally Excited Gas: Influence of Heating and Cooling

Abstract

The dynamics of unstable sound waves in a nonequilibrium vibrationally excited gas is considered with allowance for viscosity and thermal conductivity. A numerical model has been constructed and a computational tool has been developed to study the linear and nonlinear stages of the development of acoustic instability in a nonequilibrium gas with different models of relaxation, heating, and cooling times. The numerical model has a high spatial resolution and second order accuracy. It is shown that at the initial stage small disturbances generated by a sound source grow exponentially in accordance with conclusions of the linear theory. At the nonlinear stage of the development of acoustic instability, a sawtooth system of weak shock waves (SWs) is first formed; then, due to the interaction (merging) of SWs, a quasi-stationary system of high-intensity shock wave pulses (SWPs) is formed.