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 S m^−1 to 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.
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