Rayleigh-Bénard turbulence

Abstract

The classical example for thermally driven turbulence is Rayleigh-Benard (RB) flow, i.e., flow in a box heated from below and cooled from above. In this thesis three aspects of RB convection are studied: I - High Rayleigh Ra number thermal convection, II – Rotating RB convection, and III - 2D RB convection. We showed that high Ra number direct numerical simulations (DNS) are in good agreement with experimental results up to Ra = 2•1011, when the used numerical resolution is sufficient. When a simulation is underresolved the measured heat transport is too high, due to insufficient dissipation of the plumes close to the sidewall. This effect explains the difference observed between experiments and earlier DNS. Subsequently, we performed a DNS at Ra = 2•1012. The result is in good agreement with the experimental results of Ahlers et al. and Niemela et al. while there is a visible difference with the measurements of Chavanne et al.. The DNS do not show any increase in Nu/Ra1/3, neither due to Prandtl Pr number effects, nor due to a constant heat flux boundary condition at the bottom plate instead of constant temperature boundary conditions. We demonstrated that the onset of heat transport enhancement in rotating RB convection occurs with a sharp transition, which coincides with a transition between two different turbulent flow states, one dominated by a large convection roll in the whole cell for weak rotation, and one dominated by local vertically-aligned vortices for strong rotation. We showed that this sharp transition is caused by the finite size of the system and that the rotation rate at the onset of heat transport enhancement strongly depends on the aspect ratio. We analyzed the spontaneous flow reversals of the large scale circulation (LSC) in 2D RB with flow visualization experiments and DNS. For intermediate Pr there is a diagonal LSC and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner flow rolls play a crucial role for the large scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main diagonal LSC, thus leading to reversal.