Geophysical and Astrophysical Fluid Dynamics Schrinner Mean-field Concept and Direct Numerical Simulations of Rotating Magnetoconvection and the Geodynamo
Geophysical and Astrophysical Fluid Dynamics Schrinner Mean-field Concept and Direct Numerical Simulations of Rotating Magnetoconvection and the Geodynamo
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通讯作者：
M. Schrinner;K. R. Adler;D. Schmitt;M. Rheinhardt;U. Christensen
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作者：
M. Schrinner;K. R. Adler;D. Schmitt;M. Rheinhardt;U. Christensen
（200x年月00日收到；最终定稿200x年月00日）平均场理论描述了导致各种宇宙物体中大规模磁场的磁流体动力学过程。本文研究了旋转球壳中的磁对流和发电机过程。平均场是由方位平均来定义的。在平均场理论框架下，决定平均电动势传统表示形式的系数，包括平均磁场的一阶导数，是分析和模拟发电机作用的关键。本文提出了两种从上述过程的直接数值模拟中提取平均场系数的方法。第一种方法不使用内禀近似，第二种方法基于二阶相关近似。对于足够慢的流体运动，两种方法的结果是令人满意的。这两种方法都应用于旋转磁对流和准静止地球发电机的模拟。用这些系数描述的平均场感应效应，如α-效应，在这两个例子中都是高度各向异性的。在内核切线柱面外存在强γ-效应，并存在α - 2机制。在地球发电机的例子中，紊流扩散率超过分子扩散率至少一个数量级。为了将平均场模拟与相应的直接数值模拟进行比较，构建了包含所有先前确定的平均场系数的二维平均场模型。不同平均场系数组的各种试验揭示了它们的作用和意义。在这里所考虑的磁对流和地球动力学的例子中，只有当涉及大量的平均场系数时，直接数值模拟与平均场模拟之间的匹配才令人满意。在磁对流算例中，数值模拟得到的方位平均磁场与平均场模型得到的方向平均磁场吻合较好。然而，这种匹配在地球发电机的情况下不再完全令人满意。在这里，忽略平均磁场的高一阶空间导数的平均电动势的传统表示不再是一个很好的近似。
(Received 00 Month 200x; in final form 00 Month 200x) Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g. the α-effect, are highly anisotropic in both examples. An α 2-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.