Stochastic parametric excitation of thermal convection in a porous medium layer

Abstract

We study stochastic parametric excitation of free thermal convection of a fluid saturating an infinite horizontal layer or a rectangular cell of a porous medium under random modulation of gravity. The mathematical formulation we use makes it possible to explore the cases of heating both from below and above, as well as the case of low gravity conditions. Equations for the stochastic dynamics of the amplitude of small perturbations of the temperature and streamfunction fields have been obtained for the system. Conditions for the growth of the second moments have been derived for these equations; these conditions are used as a criterion for the excitation of convective motions in the system. We have verified that the obtained modes of the fastest growth of the second moments for all values of the parameters lie in a region of phase space that is physically meaningful. The heat flux, characterized by the Nusselt number, has been derived to be related to the second moment of the temperature perturbations. It follows from this that the threshold of stochastic excitation of second moments determines the threshold of excitation of convective heat transfer.