  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 lowgravity conditions. The excitation threshold of the
second moments of the current velocity and the temperature perturbations is
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 to the effect of high-frequency periodic
modulation reveals dramatic dissimilarity between the two.
