Rayleigh-Benard problem for an anomalous fluid

The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh-Benard problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically using linear theory. Numerical investigation of the spectral problem is based on the Godunov-Abramov orthogonalization method. The calculation results are compared with the well-known results for the limiting case where the density is considered a quadratic function of temperature and does not depend on pressure.