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Heat transport by coherent Rayleigh-Benard convection

机译：相干瑞利-贝纳德对流传热

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摘要

Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number Ra approximate to 1708 has been calculated up to Ra approximate to 5.10(6) and its Nusselt number is Nu similar to 0.143 Ra-0.28 with a delicate spiral structure in the temperature field. Another solution that maximizes Nu over the horizontal wavenumber has been calculated up to Ra = 10(9) and scales as Nu similar to 0.115 Ra-0.31 for 10(7) < Ra <= 10(9), quite similar to 3D turbulent data that show Nu similar to 0.105 Ra-0.31 in that range. The optimum solution is a simple yet multi-scale coherent solution whose horizontal wavenumber scales as 0.133 Ra-0.217. That solution is unstable to larger scale perturbations and in particular to mean shear flows, yet it appears to be relevant as a backbone for turbulent solutions, possibly setting the scale, strength, and spacing of elemental plumes. (C) 2015 AIP Publishing LLC.
机译：在无滑移边界条件和Prandtl数为7的情况下，获得了二维Boussinesq方程的稳定但总体上不稳定的解。从瑞利数Ra约为1708的导通状态分叉出的一次解已经计算出来，直到Ra约为5.10（6） ），其Nusselt数为Nu，类似于0.143 Ra-0.28，在温度场中具有精细的螺旋结构。已经计算出另一种在水平波数上最大化Nu的解决方案，直到Ra = 10（9）并缩放为Nu类似于10（7）

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