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Scaling of large-scale quantities in Rayleigh-Benard convection
(Indian Institute of Technology Kanpur)
Using direct numerical simulations of Rayleigh-B ́enard convection in rectangular boxes, we study the scaling of large-scale quantities such as the Nusselt (Nu) and P ́eclet (Pe) numbers for moderate Rayleigh (Ra) numbers. We observe that Nu ∼ Raγ and Pe ∼ Raζ , where γ increases from 0.27 to 0.32 and ζ from 0.43 to 0.61 when the Prandtl number is increased from 0.02 and ∞. For very large Prandtl numbers, we observed that the kinetic energy spectrum scales with wavenumber k as k−13/3 in the inertial range. Moreover, the large-scale quantities and energy spectrum show similar scalings in 2D and 3D RBC for very large Prandtl numbers. We also find that the corner rolls and the vortex reconnections are absent during a flow reversal in 2D boxes with stress-free boundary condition, whereas they play important roles during a reversal in the boxes with rigid walls.