Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions
Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions
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大瑞利数热对流：热通量预测和强非线性解决方案
DOI：
10.1063/1.3210777
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发表时间：
2009
影响因子：
4.6
通讯作者：
S. Cox
中科院分区：
文献类型：
--
作者：
G. Chini;S. Cox
本文研究了强非线性Rayleigh-Benard对流单体在大Rayleigh数和中等Prandtl数的渐近极限下的结构。与以往的无限普朗特数对流的理论研究中分析的流量，我们的细胞的解决方案表现出动态无粘性恒定涡核。通过求解单元边缘温度分布的积分方程，我们能够预测，作为单元长宽比的函数，核心涡度的值，流动的细节内的薄边界层和上升/下降的羽流相邻的对流单元的边缘，特别是，通过层的散装热通量。我们的渐近分析的结果得到证实，使用全伪谱数值模拟，并确认热通量最大化的对流细胞是大致正方形的横截面。
We investigate the structure of strongly nonlinear Rayleigh–Benard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.