Effect of the Earth's magnetic field spatial distribution on the electromagnetic coupling at the fluid core boundaries for nutations

Nutations are periodic variations in the orientation of the Earth's rotation axis in space. This motion is generated by the gravitational torque applied on the Earth's equatorial bulge by the Moon, the Sun, and the other planets. Because the mantle, the fluid outer core and the solid inner core react differently to the applied torque, the nutation motion is characterized by differential rotations between these three regions. Since the boundaries of the fluid outer core are permeated by a background magnetic field (the geodynamo field), the differential rotation at the fluid core boundaries induces a secondary magnetic field by shear and advection of the background field. The associated electric currents produce Lorentz forces and torques between the outer core, inner core, and mantle, that tend to oppose the differential rotation. A previous study has shown that the magnitude of the electromagnetic (EM) torque is mainly determined by the electrical conductivities on both sides of the outer core boundaries and by the mean RMS strength of the background magnetic field, with the spatial distribution of this magnetic field being unimportant to first order. The goal of the present work is to reassess the role of the magnetic field spatial distribution on the strength of the EM torque using a new model of the EM coupling for nutations that we have recently developed. Our model differs from previous ones in that we use a global approach to describe the induced magnetic field. Moreover, we also include in the torque the contribution from the poloidal component of the induced field, an effect neglected in previous models. In addition, we do not assume a priori that the non-dipolar components of the background magnetic field can be represented by a uniform field with the same power but instead we calculate the torque on the basis of the full geometry of the field. This is particularly important for the poloidal torque as it depends directly on the surface gradient of the radial field (and would vanish in the case of a uniform field). At the core-mantle boundary (CMB), the magnetic field can be inferred from surface observations for degrees up to 13 in spherical harmonics but the higher degrees are unknown. We test the effect of different extrapolations of the CMB magnetic field for higher degrees on the EM coupling at the CMB. At the inner core boundary, we test a wider range of magnetic field spatial distributions as even the low degrees of the field are unknown.