Sequential Transitions of the Thermal Convection in a Square Cavity

Sequential transitions of the thermal convection in a square cavity heated from below are investigated up to the time periodic state by numerical simulation. The flow field is assumed to be two-dimensional and all the boundaries are assumed to be rigid and perfectly thermal conducting as a mathematical model. The Prandtl number is fixed as P =7. Three typical solutions are found for three values of the Rayleigh number R a . To explain the results of numerical simulation, the stability of the motionless state, the nonlinear equilibrium solutions of the thermal convection, and the stability of the equilibrium states are investigated, and the bifurcation diagram is obtained for a wide range of R a . The dynamical properties of the solutions obtained by numerical simulation are proved to be explained quite well from the bifurcation diagram obtained by the stability analyses.