Linear dynamics of acoustic instability in a non-equilibrium gas: stability boundaries and forbidden frequency regions

The dynamics of small disturbances in a nonequilibrium vibrationally excited gas is considered. The wave and dispersion equations are obtained, describing the dynamics of acoustic modes in the linear approximation. The criteria for identifying physically correct solutions of the dispersion equation and determining the boundaries of the regions of forbidden frequencies of acoustic waves are formulated. These criteria allow us to exclude from consideration the regions of non-physical (“phantom”) solutions, in which the phase velocity of sound can become abnormally high and at certain frequencies turn to infinity. The dispersion properties of unstable sound waves are studied in detail, estimates of the increment are obtained, and the stability boundaries and zones of forbidden frequencies are determined depending on the degree of nonequilibrium of the medium, models of relaxation, heating and cooling. It is shown that at certain values of the degree of nonequilibrium of the medium and the dependence of the relaxation time and the cooling function on temperature and density, sound waves in a vibrationally excited gas are unstable. In this case, the acoustic incrementreaches its maximum when the period of sound waves τ𝑠 is comparable with the relaxation time τ, and in the high-frequency region of the spectrum τ𝑠 ≲ τ, due to viscosity and thermal conductivity, stabilization of acoustic instability occurs.