Scaling Laws in Rayleigh‐Bénard Convection
Scaling Laws in Rayleigh‐Bénard Convection
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DOI：
10.1029/2019ea000583
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发表时间：
2019-09
影响因子：
3.1
通讯作者：
Meredith Plumley;K. Julien
中科院分区：
文献类型：
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作者：
Meredith Plumley;K. Julien
回顾和讨论了瑞利-贝纳德对流（RBC）的传热标度理论的配置和没有旋转和磁场。标度律是研究和表征地球物理流的有用工具，因为它们为外推到目前的计算和实验努力仍然无法获得的极端参数制度提供了基础。具体而言，幂律缩放，涉及的热传输的效率，如测量的无量纲努塞尔数Nu，热驱动的追求。考虑了泛函形式Nu_（Ra/Rac）α的关系。考虑到强烈的稳定影响的旋转和磁场，热驱动被认为是在超临界的系统的瑞利数Ra的比率，测量的热强迫，临界Rac的上下文中，上面发生对流。对流，旋转对流和磁对流的制度，指数α的分析预测，和标度的基准对现有的数值和实验结果在可访问的制度。指数表明，热传输的热瓶颈内发生的热边界层的非旋转红细胞和旋转红细胞的湍流内部。对于磁对流，所有理论都得到了α=1的单一指数，并且没有发现瓶颈。
The heat transfer scaling theories for Rayleigh‐Bénard convection (RBC) are reviewed and discussed for configurations with and without rotation and magnetic fields. Scaling laws are a useful tool in studying and characterizing geophysical flows as they provide a basis for extrapolation to extreme parameter regimes that remain unobtainable by current computational and experimental efforts. Specifically, power law scalings that relate the efficiency of the heat transport, as measured by the nondimensional Nusselt number Nu, to the thermal driving are pursued. Relations of the functional form Nu∝(Ra/Rac)α are considered. Given the strongly stabilizing influences of rotation and magnetic fields, thermal driving is considered in the context of the supercriticality of the system given by the ratio of the Rayleigh number Ra, measuring the thermal forcing, to the critical Rac, above which convection occurs. Analytical predictions for the exponent α are presented for the regimes of convection, rotating convection, and magnetoconvection, and the scalings are benchmarked against available numerical and experimental results in the accessible regimes. The exponents indicate that the thermal bottleneck to heat transport occurs within the thermal boundary layers for nonrotating RBC and the turbulent interior for rotating RBC. For magnetoconvection, a single exponent of α=1 is obtained for all theories and no bottleneck is identified.