The electrical conductivity of the Earth’s core is an important physical parameter that controls the core dynamics and the thermal evolution of the Earth. In this study, the effect of core electrical conductivity on core surface flow models is investigated. Core surface flow is derived from a geomagnetic field model on the presumption that a viscous boundary layer forms at the core–mantle boundary. Inside the boundary layer, where the viscous force plays an important role in force balance, temporal variations of the magnetic field are caused by magnetic diffusion as well as motional induction. Below the boundary layer, where core flow is assumed to be in tangentially geostrophic balance or tangentially magnetostrophic balance, contributions of magnetic diffusion to temporal variation of the magnetic field are neglected. Under the constraint that the core flow is tangentially geostrophic beneath the boundary layer, the core electrical conductivity in the range from $${10}^{5} ~\mathrm{S}~{\mathrm{m}}^{-1}$$ 10 5 S m - 1 to $${10}^{7}~ \mathrm{S}~{\mathrm{m}}^{-1}$$ 10 7 S m - 1 has less significant effect on the core flow. Under the constraint that the core flow is tangentially magnetostrophic beneath the boundary layer, the influence of electrical conductivity on the core flow models can be clearly recognized; the magnitude of the mean toroidal flow does not increase or decrease, but that of the mean poloidal flow increases with an increase in core electrical conductivity. This difference arises from the Lorentz force, which can be stronger than the Coriolis force, for higher electrical conductivity, since the Lorentz force is proportional to the electrical conductivity. In other words, the Elsasser number, which represents the ratio of the Lorentz force to the Coriolis force, has an influence on the difference. The result implies that the ratio of toroidal to poloidal flow magnitudes has been changing in accordance with secular changes of rotation rate of the Earth and of core electrical conductivity due to a decrease in core temperature throughout the thermal evolution of the Earth.

中文翻译：

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岩心电导率对岩心表面流动模型的影响

地核的电导率是控制地核动力学和地球热演化的重要物理参数。在这项研究中，研究了岩心电导率对岩心表面流动模型的影响。地磁场模型推导出地核表面流动，假设在地核-地幔边界处形成粘性边界层。在边界层内，粘性力在力平衡中起着重要作用，磁场的时间变化是由磁扩散和运动感应引起的。在边界层以下，假设核心流处于切向地转平衡或切向磁转平衡，磁扩散对磁场时间变化的贡献被忽略。在边界层下核心流切向地转的约束下，核心电导率范围为 $${10}^{5} ~\mathrm{S}~{\mathrm{m}}^{-1 }$$ 10 5 S m - 1 到 $${10}^{7}~ \mathrm{S}~{\mathrm{m}}^{-1}$$ 10 7 S m - 1 的影响较小在核心流上。在边界层下核心流为切向磁自转的约束下，可以清楚地识别电导率对核心流模型的影响；平均环形流的大小不增加或减少，但平均极向流的大小随着核心电导率的增加而增加。这种差异源于洛伦兹力，洛伦兹力可能比科里奥利力更强，以获得更高的导电性，因为洛伦兹力与电导率成正比。换句话说，代表洛伦兹力与科里奥利力之比的埃尔萨瑟数对差异有影响。结果表明，由于在整个地球热演化过程中地核温度降低，环向流与极向流的比值一直随着地球自转速率和地核电导率的长期变化而变化。