Subcritical dynamos in rapidly rotating planar convection
Subcritical dynamos in rapidly rotating planar convection
复制标题
DOI：
10.1103/physrevfluids.5.113702
复制
发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
R. G. Cooper;P. Bushby;C. Guervilly
中科院分区：
文献类型：
--
作者：
R. G. Cooper;P. Bushby;C. Guervilly
我们研究发电机行动使用数值模拟的平面Boussinesq对流在快速旋转（低埃克曼数，Ek），重点是亚临界发电机行动，其中发电机是持续的瑞利数，Ra，低于临界瑞利数的开始对流，Ra$_c$。这些解决方案是通过首先调查的超临界状态，其中发电机能够产生一个大规模的磁场，显着影响对流运动，与相关的埃尔萨瑟数的顺序Ek$^{1/3}$。然后通过跟踪该溶液分支进入亚临界状态，取超临界溶液，然后逐渐降低相应的瑞利数，找到亚临界溶液。我们表明，减少Ekman数导致扩展的亚临界范围的Ra/Ra$_c$，下降到最佳值Ek$=10^{-5}$。对于磁普朗特数的顺序统一，亚临界，然后阻碍了在较低的埃克曼数时，由较小尺度对流驱动的发电机产生相对较强的大尺度磁场时，出现的大尺度模式。大规模模式无法维持发电机的行动导致间歇性的行为，似乎抑制亚临界。亚临界解也对磁雷诺数（或等效地，磁普朗特数，Pm）的值敏感，因为需要大于70的磁雷诺数的值来产生发电机动作，但是大的值导致能够将系统推离亚临界分支太远并且朝向平凡传导状态的波动。
We study dynamo action using numerical simulations of planar Boussinesq convection at rapid rotation (low Ekman numbers, Ek), focusing on subcritical dynamo action in which the dynamo is sustained for Rayleigh numbers, Ra, below the critical Rayleigh number for the onset of nonmagnetic convection, Ra$_c$. These solutions are found by first investigating the supercritical regime, in which the dynamo is able to generate a large-scale magnetic field that significantly influences the convective motions, with an associated Elsasser number of order Ek$^{1/3}$. Subcritical solutions are then found by tracking this solution branch into the subcritical regime, taking a supercritical solution and then gradually lowering the corresponding Rayleigh number. We show that decreasing the Ekman number leads to an extension of the subcritical range of Ra/Ra$_c$, down to an optimal value of Ek$=10^{-5}$. For magnetic Prandtl numbers of order unity, subcriticality is then hampered by the emergence of a large-scale mode at lower Ekman numbers when the dynamo driven by the smaller scale convection generates relatively stronger large-scale magnetic field. The inability of the large-scale mode to sustain dynamo action leads to an intermittent behaviour that appears to inhibit subcriticality. The subcritical solutions are also sensitive to the value of the magnetic Reynolds number (or equivalently, the magnetic Prandtl number, Pm), as values of the magnetic Reynolds number greater than 70 are required to produce dynamo action, but large values lead to fluctuations that are able to push the system too far from the subcritical branch and towards the trivial conducting state.