Shock wave structures in an isentropically unstable heat-releasing gas

In this work, we analytically and numerically investigate the types of stationary gasdynamic waves formed in a heat-releasing medium with isentropic (acoustic) instability. As the mathematical model, the system of one-dimensional gasdynamic equations is used, in which the heating and cooling processes are taken into account using the generalized heat-loss function. Our analysis reveals that the type of stationary structures depends on their velocity W and heating/cooling processes acting in the medium. In an isentropically unstable medium, it is shown that the type of structures depends on whether they propagate faster or slower than the critical velocity W-cr. If W > W-cr, a shock wave is formed, in which, after the shock-wave compression, the gas expands to a stationary value. The characteristic size of the expansion region depends on the characteristic heating time, which is determined by the specific type of the heat-loss function. If W < W-cr, the shock wave turns out to be unstable and decays into a sequence of autowave (self-sustaining) pulses. The amplitude and velocity (W = W-cr) of the autowave pulse, found analytically in the article, are also determined by the type of the heat-loss function. The comparison of analytical predictions of the developed method with the results of nonlinear equation previously obtained using the perturbation theory, as well as with the numerical simulations, confirms the high accuracy of the method. Published under an exclusive license by AIP Publishing.