Rayleigh–Taylor Instability during the Motion of Water Layer in High-Temperature Rock

We use the method of normal modes to investigate the stability of water layer flow above a region of superheated vapor in high-temperature rock. We assume that the motion occurs under the gravity and that the vapor is an imperfect gas. A numerical analysis of the obtained dispersion relation is carried out, and asymptotics are investigated in the limiting case of short-wave perturbations. The ranges of parameters in which long-wave and short-wave instabilities exist are determined. In the case of long-wave instability, we estimate the characteristic size of the most unstable perturbation.