Large-amplitude Bénard convection
Large-amplitude Bénard convection
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大振幅贝纳德对流
DOI：
10.1017/s0022112066001083
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发表时间：
1966
影响因子：
3.7
通讯作者：
G. Veronis
中科院分区：
文献类型：
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作者：
G. Veronis
给出了在瑞利数和普朗特数范围内自由边界面间二维b<s:1>纳德对流的计算。将变量展开成由稳定性问题的特征函数组成的一系列，并将系统截断以只考虑有限数量的项。本征函数的振幅是由所得非线性方程的数值积分来计算的。在所有考虑的情况下，系统达到稳定状态，运动由单个大单元组成。在0.01 ~ 100普朗特数范围内，给出了Nusselt数与Rayleigh数的对比结果，表明热流密度随普朗特数的减小而略有增加。在瑞利数范围重叠的情况下，计算结果与郭的计算结果一致。基于湍流边界层存在的假设，给出了一个简单的启发式论证，后者的结论表明，热流密度应随着普朗特数的减小而减小。因此，这种行为在性质上不同于计算的行为。其原因似乎与这样一个事实有关，即在计算的情况下，单个大细胞使流体能够通过重复循环加速，直到达到一种稳定状态，其运动幅度远远大于单个湍流团在引力场中自由落体所能获得的运动幅度。
Calculations are presented for two-dimensional Bénard convection between free bounding surfaces for ranges of Rayleigh and Prandtl numbers. The variables are expanded in a series consisting of the eigenfunctions of the stability problem and the system is truncated to take into account only a limited number of terms. The amplitudes of the eigenfunctions are evaluated by numerical integration of the resulting non-linear equations. In all cases considered, the system achieves a steady state with the motion consisting of a single large cell. Results for Nusselt number vs. Rayleigh number are given for a range of Prandtl number varying between 0·01 and 100 and show that heat flux increases slightly with decreasing Prandtl number. The calculations agree with those of Kuo where the ranges of Rayleigh number overlap. A simple heuristic argument based on the assumption that turbulent boundary layers exist is also given and the conclusions of the latter indicate that heat flux should decrease with decreasing Prandtl number. Thus the behaviour is qualitatively different from that of the calculations. The reason appears to be associated with the fact that the single large cell in the computed cases enables the fluid to accelerate through repeated cycles until it achieves a steady state with the amplitude of the motion much larger than could be acquired by a single turbulent blob free-falling in the gravitational field.