快速旋转渐近区中的球形对流发电机
Spherical convective dynamos in the rapidly rotating asymptotic regime
摘要：
在行星系中的自持对流发电机在快速旋转的渐近状态下运行，其中科里奥利力、压力、浮力和洛伦兹力之间保持平衡（MAC平衡）。经典的数值解以前已获得的制度中的适度旋转的粘性和惯性力仍然显着。我们定义了一个一维路径之间的经典模型和渐近条件的要求，以执行MAC平衡和保持磁扩散和对流翻转时间（磁雷诺数）之间的比率参数空间。沿着这条路径进行的直接数值模拟表明，在尺度大于磁耗散长度的解决方案的空间结构在很大程度上是不变的。这使得大涡模拟的定义基于这样的假设，即流体动力学湍流的小尺度细节与大尺度渐近状态的确定无关。这些模拟被证明是在良好的协议与直接模拟的范围内，两者都是可行的，并可以计算出的控制参数值远远超出了目前的技术水平，如埃克曼数$E=10^{-8}$。我们得到强场对流发电机接近MAC平衡和泰勒状态到前所未有的准确度。经典模型和渐近条件之间的物理连接被证明是缺乏突然的转变，表现出经典的数值发电机机制的渐近相关性。系统的领域被证实遵循无扩散，功率为基础的标度律沿路径。
英文摘要：
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.
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