Two-dimensional Rayleigh-Benard convection
Two-dimensional Rayleigh-Benard convection
复制标题
二维瑞利-贝纳德对流
DOI：
10.1017/s0022112073002600
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发表时间：
1973
影响因子：
3.7
通讯作者：
N. Weiss
中科院分区：
文献类型：
--
作者：
D. Moore;N. Weiss
通过一系列数值实验研究了自由边界间Boussinesq流体的二维对流问题。早期的计算由弗洛姆和Veronis被限制为最大瑞利数R 50倍的临界值R，线性不稳定。该范围扩展到1000 Rc。本文系统地研究了普朗特数p = 6.8的水的对流，以及普朗特数在0.01和无穷大之间的其他模型。两种不同的模式的非线性行为的区别。对于普朗特数大于1有一个粘性制度，其中努塞尔数$N \approx 2（R/R_c）^{\frac{1}{3}}$，独立于p。热通量是最大的细胞，其宽度是1·2和1·4倍的层深度。当$5 \leqslant R/R_c \lesssim p^{\frac{3}{2}}$。在较高的瑞利数下，涡度平流变得重要，N ∞ R 0·365。当p = 6·8时，正方形单元的热通量最大;对于更宽的单元，稳定的对流是不可能的，而是出现有限振幅的振荡，层中温度和速度的周期性波动。当p < 1时，还发现N ∞ R 0·365，当p [Lt ] 1时，比例常数等于1·90，随着p的增加而缓慢减小。在这些制度的物理行为进行了分析，并与天体物理对流。
Two-dimensional convection in a Boussinesq fluid confined between free boundaries is studied in a series of numerical experiments. Earlier calculations by Fromm and Veronis were limited to a maximum Rayleigh number R 50 times the critical value R, for linear instability. This range is extended to 1000Rc. Convection in water, with a Prandtl number p = 6·8, is systematically investigated, together with other models for Prandtl numbers between 0·01 and infinity. Two different modes of nonlinear behaviour are distinguished. For Prandtl numbers greater than unity there is a viscous regime in which the Nusselt number $N \approx 2(R/R_c)^{\frac{1}{3}}$, independently of p. The heat flux is a maximum for cells whose width is between 1·2 and 1·4 times the layer depth. This regime is found when $5 \leqslant R/R_c \lesssim p^{\frac{3}{2}}$. At higher Rayleigh numbers advection of vorticity becomes important and N ∞ R0·365. When p = 6·8 the heat flux is a maximum for square cells; steady convection is impossible for wider cells and finite amplitude oscillations appear instead, with periodic fluctuations of temperature and velocity in the layer. For p < 1 it is also found that N ∞ R0·365, with a constant of proportionality equal to 1·90 when p [Lt ] 1 and decreasing slowly as p is increased. The physical behaviour in these regimes is analysed and related to astrophysical convection.