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<p>We use the method of normal modes to investigate the stability of water layer flow above a&#xa0;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&#xa0;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.</p>

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

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  • 发表日期：

    2026年4月1日

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  • K. R. Zhitnikov,
  • G. G. Tsypkin

摘要

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.