Large-scale balances and asymptotic scaling behaviour in spherical dynamos
Large-scale balances and asymptotic scaling behaviour in spherical dynamos
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DOI：
10.1093/gji/ggab274
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发表时间：
2021-08-04
影响因子：
2.8
通讯作者：
Featherstone, Nicholas A.
中科院分区：
文献类型：
--
作者：
Calkins, Michael A.;Orvedahl, Ryan J.;Featherstone, Nicholas A.
利用数值模拟数据和渐近理论分析了与地球发电机相关的球壳中对流驱动发电机的大尺度动力学。尝试确定力的渐近大小（小参数为艾克曼数 Ek）以及相关的速度和磁场。与之前的工作一致，主要的平均力平衡是子午面的热风（科里奥利、压力梯度和浮力）和纬向的科里奥利-洛伦兹。据观察，在一定范围的 Ek 和热力作用下，洛伦兹力弱于平均浮力；在所研究的参数空间内，这些力的相对差异似乎为 O(Ek(1/6))。我们发现热风平衡要求平均纬向速度为 O(Ek(-1/3))，而经向环流则渐近地小 O(Ek(1/6)) 倍。平均温度方程显示了热扩散和对流热通量发散之间的平衡，表明存在大小为 O(Ek(1/6)) 的平均温度长度尺度。尽管模拟数据显示平均磁场长度尺度为 O(Ek(1/6))，但平均磁场和脉动磁场均未表现出对 Ekman 数的强烈依赖性。力的渐进排序的结果是，尽管不存在前导磁致平衡，但泰勒约束的精度满足 O(Ek(1/6))。关于对地球发电机很重要的大规模流动，讨论了力平衡的进一步后果。
The large-scale dynamics of convection-driven dynamos in a spherical shell, as relevant to the geodynamo, is analysed with numerical simulation data and asymptotic theory. An attempt is made to determine the asymptotic size (with the small parameter being the Ekman number, Ek) of the forces, and the associated velocity and magnetic fields. In agreement with previous work, the leading order mean force balance is shown to be thermal wind (Coriolis, pressure gradient and buoyancy) in the meridional plane and Coriolis-Lorentz in the zonal direction. The Lorentz force is observed to be weaker than the mean buoyancy force across a range of Ek and thermal forcing; the relative difference in these forces appears to be O(Ek(1/6)) within the parameter space investigated. We find that the thermal wind balance requires that the mean zonal velocity scales as O(Ek(-1/3)), whereas the meridional circulation is asymptotically smaller by a factor of O(Ek(1/6)). The mean temperature equation shows a balance between thermal diffusion and the divergence of the convective heat flux, indicating the presence of a mean temperature length scale of size O(Ek(1/6)). Neither the mean nor the fluctuating magnetic field show a strong dependence on the Ekman number, though the simulation data shows evidence of a mean magnetic field length scale of size O(Ek(1/6)). A consequence of the asymptotic ordering of the forces is that Taylor's constraint is satisfied to accuracy O(Ek(1/6)), despite the absence of a leading-order magnetostrophic balance. Further consequences of the force balance are discussed with respect to the large-scale flows thought to be important for the geodynamo.