Flow Characteristics and Structures of Three-Dimensional Unsteady Thermal Convection in a Container

In this study, we numerically investigates the flow and thermal characteristics of the three-dimensional thermal convection in a cubic cavity heated below in the gravitational field, concerning about spatially-averaged kinetic energy K, Nusselt number Nu and flow structure. We assume Prandtl number Pr = 7.1 (water) and Rayleigh number Ra = 1.0×10⁴ – 3.5×10⁵. As a result, we have specified two of three important values of the Rayleigh number which demarcate different flow bifurcations and are referred to as the second and third critical Rayleigh numbers Ra_c2 and Ra_c3. We have found that Ra_c2 and Ra_c3 are roughly 2.6×10⁵ and 3.1×10⁵, respectively. We have observed a histerisis effect upon the value of Ra_c2 with chaotic behaviour at Ra ≈ Ra_c2, and revealed flow structures. In addition, we investigate the relationship between Ra and the oscillatory-convection frequency. The increasing rate of the K_mean with increasing Ra shows a different manner from that of Nu_{inflow-ave, mean}. That is, the former is progressive and the latter is asymptotic, as Ra increases. Both the values of K_mean and Nu_{inflow-ave, mean} in oscillatory flow tend to be smaller than those in steady flow, respectively. Then, there exist small jumps/drops of K_mean and Nu_{inflow-ave, mean} at Ra = Ra_c2.