Abstract
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} to {10}^{7}~ mathrm{S}~{mathrm{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.
Highlights
The intrinsic magnetic field of the Earth is generated by dynamo action due to electromagnetic fluid motion in the outer core, the main components of which are iron and nickel
Core elec trical conductivity is related to two terms in the equa tion to be solved: the magnetic diffusion term in the induction equation and the Lorentz force term in the Navier–Stokes equation
Geostrophic and tangentially magnetostrophic constraints were imposed for core flow beneath the viscous boundary layer at the core–mantle boundary to derive a core surface flow model from a geomagnetic field model
Summary
The intrinsic magnetic field of the Earth is generated by dynamo action due to electromagnetic fluid motion in the outer core, the main components of which are iron and nickel. It is essential that the motional induction overcomes the magnetic diffusion through Ohmic dis sipation to maintain the geomagnetic field. The Earth has pos sessed its intrinsic magnetic field generated by the geo dynamo since around 3.45 Ga (Tarduno et al 2010). Noticeable columnar convective structures parallel to the rotational axis of the Earth are found to explain the generation mechanism of the axial dipole magnetic field (e.g., Kageyama and Sato 1997; Olson et al 1999). Numerical geo dynamo models have succeeded in explaining certain properties of the geomagnetic field, such as the domi nance of the dipole field, and secular variations includ ing polarity reversals (e.g., Christensen and Wicht 2015). The convective motions produced by numerical simulations do not necessarily show proper core dynam ics, mainly because the parameters adopted in numerical simulations are far from the real ones
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