Characteristic Times of Acoustic and Condensation Instability in Heat-releasing Gas Media

We investigate wave evolution in gas media with non-adiabatic heating and cooling processes depending on temperature and density. In this work, the temporal instability of acoustic disturbances in a heat-releasing uniform gas medium is under consideration. We neglect the influence of shear viscosity and thermal conduction. During the investigation, we describe the dispersion relation for the dynamics of two acoustic modes propagating in opposite directions and condensation (thermal) mode. The condensation mode has purely imaginary frequency and describes local changes of temperature and density under constant pressure. Furthermore, analytical expressions for temporal increments of acoustic and condensation modes are obtained. Features of obtained solutions depending on the ratio of low- and high-frequency adiabatic indexes are shown. The relationship between the acoustic temporal increment and the second (bulk) viscosity coefficient is described as well.