Probabilistic structure of the geodynamo
Probabilistic structure of the geodynamo
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DOI：
10.1103/physreve.98.063112
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发表时间：
2018-04
影响因子：
2.4
通讯作者：
C. Scullard;B. Buffett
中科院分区：
文献类型：
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作者：
C. Scullard;B. Buffett
作者：Scullard，CR; Buffett，BA|摘要：© 2018美国物理学会。地球轴向磁偶极场最有趣的特征之一，从地质记录中众所周知，是其偶尔和不可预测的极性反转。理解这种现象是非常困难的高度非线性本质的基本磁流体动力学问题。对再生发生的液体外核的数值模拟只能模拟远离地球的条件。在分析方面，情况也好不到哪里去;基本的计算，例如将平均逆转率与各种核心参数联系起来，显然是难以处理的。在这里，我们提出了一个解决这些问题的框架。从磁感应方程开始，我们表明，通过考虑其源是随机过程具有相当普遍的属性，我们可以推导出一个微分方程的联合概率分布的主导环向和极向模式。这可以简化为一个福克-普朗克方程，并在绝热近似的帮助下，进一步减少到一个方程的偶极振幅。根据这些方程，与磁场有关的各种量，包括平均反转率、场强和完成反转的时间，可以作为少量数值参数的函数来计算。这些参数又可以从物理考虑或古地磁，数值和实验数据的约束计算。
Author(s): Scullard, CR; Buffett, BA | Abstract: © 2018 American Physical Society. One of the most intriguing features of Earth's axial magnetic dipole field, well known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the highly nonlinear nature of the underlying magnetohydrodynamic problem. Numerical simulations of the liquid outer core, where regeneration occurs, are only able to model conditions that are far from Earth-like. On the analytical front, the situation is not much better; basic calculations, such as relating the average rate of reversals to various core parameters, have apparently been intractable. Here, we present a framework for solving such problems. Starting with the magnetic induction equation, we show that by considering its sources to be stochastic processes with fairly general properties, we can derive a differential equation for the joint probability distribution of the dominant toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation and, with the help of an adiabatic approximation, reduced even further to an equation for the dipole amplitude alone. From these equations various quantities related to the magnetic field, including the average reversal rate, field strength, and time to complete a reversal, can be computed as functions of a small number of numerical parameters. These parameters in turn can be computed from physical considerations or constrained by paleomagnetic, numerical, and experimental data.