Title: Asymptotics of spherical dynamos exhibiting a small-scale MAC balance Show Chinese title

Title: 球形发电机的渐近行为表现出小尺度MAC平衡

Abstract: Understanding the asymptotic behaviour of numerical dynamo models is critical for extrapolating results to the physical conditions that characterise terrestrial planetary cores. Here we investigate the behaviour of convection-driven dynamos reaching a MAC (magnetic-Archimedes-Coriolis) balance on the convective length scale and compare the results with non-magnetic convection cases. In particular, the dependence of physical quantities on the Ekman number, $Ek$, is studied in detail. The scaling of velocity dependent quantities is observed to be independent of the force balance and in agreement with quasi-geostrophic theory. The primary difference between dynamo and non-magnetic cases is that the fluctuating temperature is order unity in the former such that the buoyancy force scales with the Coriolis force. The MAC state yields a scaling for the flow speeds that is identical to the so-called CIA (Coriolis-inertia-Archimedes) scaling. There is an $O(Ek^{1/3})$ length scale present within the velocity field irrespective of the leading order force balance. This length scale is consistent with the asymptotic scaling of the terms of the governing equations and is not an indication that viscosity plays a dominant role. The peak of the kinetic energy spectrum and the ohmic dissipation length scale both exhibit an Ekman number dependence of approximately $Ek^{1/6}$, which is consistent with a scaling of $Rm^{-1/2}$, where $Rm$ is the magnetic Reynolds number. For the dynamos, advection remains comparable to, and scales similarly with, both inertia and viscosity, implying that nonlinear convective Rossby waves play an important role in the dynamics even in a MAC regime. Show Chinese abstract

Abstract: 理解数值地磁模型的渐近行为对于将结果外推到表征地球行星核的物理条件至关重要。 在这里，我们研究了在对流长度尺度上达到MAC（磁场-阿基米德-科里奥利）平衡的对流驱动地磁模型的行为，并将结果与无磁场对流情况进行了比较。 特别是，物理量对Ekman数，$Ek$的依赖性得到了详细研究。 观察到速度相关量的标度与力平衡无关，并且与准地转理论一致。 地磁和无磁场情况之间的主要区别在于，在前者中波动温度为一阶量，因此浮力与科里奥利力成比例。 MAC状态给出了与所谓的CIA（科里奥利-惯性-阿基米德）标度相同的流动速度标度。 无论主要力平衡如何，速度场中都存在一个$O(Ek^{1/3})$长度尺度。 这个长度尺度与控制方程项的渐近标度一致，并不表示粘性起主导作用。 动能谱的峰值和欧姆耗散长度尺度均表现出大约$Ek^{1/6}$的Ekman数依赖性，这与$Rm^{-1/2}$的标度一致，其中$Rm$是磁雷诺数。 对于地磁模型，平流仍然与惯性和粘性相当，并且以类似的方式进行标度，这意味着非线性对流罗斯比波在动力学中起着重要作用，即使在MAC区域也是如此。