Numerical simulation of thermal fluid instability between two horizontal parallel plates

The buoyancy-induced thermal fluid instability between two parallel horizontal plates has been investigated numerically by solving the governing equations of base and perturbation fields using a fractional algorithm, in which the fourth-order Adams scheme and the Bi-CGSTAB scheme are embedded. An initial assumption of the perturbed temperature was made by a Gaussian random number generator. A primitive static fluid with Prandtl number 0.73 was induced to flow in the gap between the two horizontal parallel plates for three different cases: top heating, bottom heating and heating from both plates. The kinetic energy of induced flow in each vertical section and in the whole domain was calculated. The results can demonstrate whether the thermal fluid flow is stable or unstable. A linear decaying behavior is found after the initial stage. The total fluid kinetic energy in the domain converges for the top heating case, but diverges for the other two heating cases.