Overstability of acoustic waves in heat-releasing gaseous media

Abstract

The properties of acoustic waves in the heat-releasing gaseous media are under investigation. For the stationary state to be set in the medium, some balance between heating and cooling processes has to be stated. In the general case, rates of heating and cooling processes, which take place in gaseous media, may be some functions of such thermodynamic parameters as density and temperature. The temperature and density dependence of these non-adiabatic processes, in its turn, gives possibility for the positive/negative feedback between perturbations and medium to occur. If the positive feedback is stated, then overstability of acoustic and/or entropy waves takes place. The overstability conditions for acoustic and entropy mode was originally obtained by Field in his pioneer work. These conditions are known and as isentropic, isochoric and isobaric thermal instabilities and named after the type of the perturbation they primarily affect. These conditions are defined by the derivatives of the heat-loss function, which is the difference of cooling and heating rates. In this work, we analyze dispersion properties of acoustic waves for some specific combinations of these instability conditions. We show that overstability of acoustic and entropy modes in the case of simultaneous realization of isochoric, isobaric and isentropic instabilities may be accompanied by the occurrence of the propagation cut-off wavelength for acoustic waves. Moreover, the propagation cut-off wavelength for acoustic waves may occur in the thermally stable medium. Furthermore, it has been shown analytically that in cases of isobaric instability or isochoric instability (i.e. for some specific heating and cooling mechanisms) the wavelength range of non-propagating acoustic waves may also exist. The cut-off wavelengths for these cases have been obtained analytically.