Dynamics of small perturbations in a nonequilibrium vibrationally excited gas

In a linear approximation, a mathematical model of a nonequilibrium vibrationally excited gas with an exponential relaxation model has been constructed, taking into account the dependence of the parameters of an acoustically active medium (relaxation time, heating and cooling functions) on density and temperature. The dispersion properties of unstable sound and entropy modes were studied, estimates of the acoustic increment were obtained, and the limits of stability of small disturbances were determined depending on the degree of nonequilibrium of the medium (heating intensity), relaxation and cooling models. It was found that the parameters of the linear model, which determine the dependence of the heating and cooling functions on density and temperature, have a strong influence on both the acoustic increment and the phase velocity of unstable sound waves. It is shown that at certain values of the heating intensity and parameters of the cooling function, the speed of sound turns out to be abnormally high both in the low-frequency region of the spectrum (sound-infrasound) and for high-frequency harmonics (sound-ultrasound).