Stochastic parametric excitation of convective heat transfer

We study the parametric excitation of the free thermal convection in a horizontal layer and a rectangular cell by random vertical vibrations. The mathematical formulation we use allows one to explore the cases of heating from below and above and the low-gravity conditions. The excitation threshold of the second moments of the current velocity and the temperature perturbations are derived. The heat flux through the system quantified by the Nusselt number is reported to be related to the second moment of temperature perturbations; therefore, the threshold of the stochastic excitation of second moments gives the threshold for the excitation of the convective heat transfer. Comparison of the stochastic parametric excitation with the effect of high-frequency periodic modulation reveals dramatic dissimilarity between the two. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.