Stochastic parametric excitation of Rayleigh-Bénard convection

Abstract

The paper is devoted to the problem of the thermal convection excitation in a horizontal layer with isothermal free boundaries caused by a random modulation of the gravity acceleration. Equations for the stochastic dynamics of the amplitude of small perturbations of the temperature field and the stream function are derived for the system. For these equations, the conditions for the growth of mean-square values are derived; these conditions are used as a criterion for the excitation of convective motions in the system. The excitation of flows is considered both for the case of heating from below and for heating from above. It is verified that, for any parameter values, the obtained modes of the fastest growth of mean-square values lie within the physically meaningful domain of the phase space. In contrast to the case of high-frequency periodic vibrations, white Gaussian noise always exerts a destabilizing effect on the heat-conducting state of the system. The cases of white Gaussian noise and harmonic high-frequency vibrations are also compared in a general form, without reference to a particular form of thermal convection equations.