Direct numerical simulation of Rayleigh-Bénard convection in a cylindrical container of aspect ratio 1 for moderate Prandtl number fluid

A series of three-dimensional numerical simulations were conducted for the Rayleigh-Bénard convection in a cylindrical container with the aspect ratio Γ = 1. The Prandtl number of the fluid is 7 and the Rayleigh number varies from 103 to 105. Results show that the aspect ratio of the cylinder has an important influence on the multiplicity of the steady flow state. The sidewall of the cylinder at Γ = 1 restricts the increase of the number of rolls in the fluid layer. Therefore, only two-roll and single-roll flow patterns are observed at the whole simulation range of the Rayleigh number. During the transition of the Rayleigh-Bénard convection to the unsteady flow, it is found that the unsteady flow pattern and the bifurcation sequence of the oscillation flow are very sensitive to the initial condition.