Accuracy of the mean field approximation and the physical effect of Prandtl number in Bénard convection

The mean field equations, which contain no explicit Prandtl number dependence, are shown to provide reasonably accurate predictions of average heat transport for Rayleigh numbers from 2000 to 18000 over a wide range of Prandtl numbers, provided physically observed wavenumbers are used in the calculations. It is concluded from this that the physical significance of Prandtl number in Bénard convection is principally in setting the ’’preferred’’ wavenumber, i.e., the size of the convection cell.