The finite-amplitude B{\'e}nard convection problem is investigated by numerical integration of the rigid-boundary Boussinesq equations in two and three space dimensions. Solutions are obtained for a wide range of Prandtl numbers and at moderate Rayleigh numbers for which the flow is observed to approach a two-dimensional steady state. Detailed quantitative comparisons are made with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number and to determine the effect of changing cell size on the heat transport. The three-dimensional model shows good evidence of being able to yield realistic values of the cell wavelength, while the two-dimensional models yield wavelengths that are much too short. These results strongly suggest that the increase in wavelength is determined by a three-dimensional transient process, while the convection tends to a two-dimensional steady state. The increase in cell size is shown to be responsible for a substantial part of the discrepancy between previous theoretical-numerical and experimental determinations of Nusselt number. It also provides a plausible explanation for the experimentally observed dependence of heat transport on Prandtl number.

}, isbn = {1070-6631}, doi = {10.1063/1.1693502}, url = {