The influence of random temperature modulation on the convective instability

Bénard convection is considered under the influence of randomly modulated surface temperature. Using Galerkin's method the linearized stochastic dynamical equations for the Fourier modes are stated. The stability is decided by means of the corresponding moment equations and discussed for the two-mode case analytically. It is shown that the onset of instability is always advanced and depends significantly on the Prandtl number and the strength of the temperature fluctuations.