Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds
Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds
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地球表面和行星水世界附近电动力学的数学模型
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发表时间：
2017
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通讯作者：
R. Tyler
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文献类型：
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作者：
R. Tyler
具有水圈的行星体的一个有趣的特征是在球表面附近存在导电壳。这种导电壳通常位于相对绝缘的岩石、冰或大气之间，对大规模电流的流动产生强烈的约束。壳体的全部或部分可以相对于旋转行星磁场（以及由于外部物体产生的磁场）的主要分量处于流体运动中，从而产生原本不存在的运动感应电流。因此，人们可以期望在发生的电动过程的类型中的区别特征，以及施加有效地解决这类应用的专门数学方法的机会。本文的目的是介绍和讨论这种专门的方法。具体而言，薄壳近似的电动力学和流体动力学相结合，以获得简化的数学公式描述这些电流的行为，以及它们相关的电场和磁场。这些简化的公式允许解析解具有不同方面的薄壳电动力学在理想情况下。一个高效的数值方法也提出了非均匀参数分布下的计算是有用的。最后，评价了这种数学方法的优点和局限性。这种评估主要是为一般情况下的机构与水的世界或其他薄的球形导电壳。更具体的讨论给出了地球的情况下，但也木卫二和其他卫星与怀疑海洋。马里兰州大学帕克分校天文系和美国宇航局戈达德太空飞行中心大地测量和地球物理实验室，代码61 A，绿地，MD 20771电子邮件：robert.h.泰勒;电话：301-614-6472 nasa.gov
An interesting feature of planetary bodies with hydrospheres is the presence of an electrically conducting shell near the global surface. This conducting shell may typically lie between relatively insulating rock, ice, or atmosphere, creating a strong constraint on the flow of large-scale electric currents. All or parts of the shell may be in fluid motion relative to main components of the rotating planetary magnetic field (as well as the magnetic fields due to external bodies), creating motionally-induced electric currents that would not otherwise be present. As such, one may expect distinguishing features in the types of electrodynamic processes that occur, as well as an opportunity for imposing specialized mathematical methods that efficiently address this class of application. The purpose of this paper is to present and discuss such specialized methods. Specifically, thin-shell approximations for both the electrodynamics and fluid dynamics are combined to derive simplified mathematical formulations describing the behavior of these electric currents as well as their associated electric and magnetic fields. These simplified formulae allow analytical solutions featuring distinct aspects of the thin-shell electrodynamics in idealized cases. A highly efficient numerical method is also presented that is useful for calculations under inhomogeneous parameter distributions. Finally, the advantages as well as limitations in using this mathematical approach are evaluated. This evaluation is presented primarily for the generic case of bodies with water worlds or other thin spherical conducting shells. More specific discussion is given for the case of Earth, but also Europa and other satellites with suspected oceans. Department of Astronomy, University of Maryland at College Park and NASA Goddard Space Flight Center Geodesy and Geophysics Laboratory, Code 61A, Greenbelt, MD 20771 Email: robert.h.tyler@nasa.gov; Tel: 301-614-6472