Three-dimensional numerical simulation of convection in low-Prandtl-number fluids

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Abstract
We present three-dimensional numerical simulations of convection in a low-Prandtlnumber fluid confined between two infinite horizontal bounding surfaces maintained at constant temperatures. We consider the case of free-slip boundary conditions for a fluid of Prandtl number Pr = 0.2 and that of rigid boundary conditions with Pr = 0.025. In the former situation, we observe stationary, periodic, biperiodic and chaotic regimes as the Rayleigh number is increased. In the later situation, the dynamics involves very different characteristic times, and only stationary and time-periodic solutions have been simulated. Convergence to the later regime may occur after a long transient where the amplitude of the oscillation is slowly modulated.