A numerical study of thermal convection between rigid horizontal boundaries

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Abstract
A sequence of two-dimensional numerical models of Bénard convection between rigid horizontal boundaries is presented. Steady solutions were obtained in the Rayleigh number range 5125.5≦R≦512550 or 3≦R/Rc ≦300 for constant property, and infinite Prandtl number, Boussinesq fluids with unit aspect ratios. At higher values of the Rayleigh number time-dependent flow was found to occur. The rigid boundary convection solutions are compared with the predictions of boundary layer theory (blt) for rigid boundaries, laboratory experiments (between rigid boundaries), previous numerical solutions at lower R, and with numerical solutions of convection at high Rayleigh number between free boundaries. The predicted variation of the Nusselt number, Nu, with Rayleigh number, agrees well with laboratory studies, and is in excellent agreement both with previous numerical studies in the lower range R/Rc ≦20, and with bit predictions at high R. Finally, the rigid boundary scheme is used to model both the stress distribution and subsidence occurring from transient flow in the sub-continental lithosphere.