Abstract
The flow in a convectively unstable layer of fluid may be strongly influenced by large-scale ascent or descent. We consider cellular convection between horizontal surfaces on which vertical velocity is maintained at a constant value. Using an efficient numerical model to simulate the evolution of the convection in three space dimensions and time, we investigate the effect of the imposed vertical velocity on the flow.
For moderately supercritical values of the Rayleigh number and for Prandtl numbers near unity, convection is known to occur in the form of steady rolls if the specified mean vertical motion is zero, i.e., in the case of the conventional Bénard problem for a Boussinesq fluid. Our model also produces rolls under these circumstances. For sufficiently large values of the imposed vertical velocity, however, the numerically simulated rolls are replaced by polygonal cells in which the direction of flow depends on whether ascent or descent is prescribed at the boundaries, in accordance with recent theoretical and laboratory results of R. Krishnamurti. We have also investigated the dependence of the convection on the Rayleigh and Prandtl numbers within limited ranges of these parameters, and we discuss several aspects of agreement and disagreement among analytical theory, laboratory experiment and numerical simulation.
