Electromagnetic coupling and the toroidal magnetic field at the core-mantle boundary

SUMMARY Owing to exchanges of angular momentum between the Earth’s fluid outer core and the overlying solid mantle, the Earth’s rotational rate fluctuates on periods of a few years to a few decades. However, the mechanism which allows the exchange of angular momentum is not understood. Here we examine the possibility that core-mantle coupling is predominantly electromagnetic and thus responsible for the decadal length of day variations. The electromagnetic couple on the mantle can be divided into poloidal and toroidal parts, and, by requiring continuity of the horizontal component of the electric field at the core-mantle boundary, the toroidal couple can be divided into separate advective and leakage parts. The poloidal couple results entirely from the interaction of the poloidal field with currents induced by its time variation; the advective couple results from the dragging of poloidal field lines through a conducting mantle; and the leakage couple results from the diffusion of toroidal magnetic field from the core’s interior into the mantle. The poloidal and advective couples can be estimated by using models of the downward continued poloidal field and models of the core velocity. We find that neither the poloidal couple nor the advective couple exhibit sufficient variability to account for the decadal length of day variations. If this is true, and if core-mantle coupling is indeed predominantly electromagnetic, then most of the variability in the length of day must result from the leakage couple, which, unfortunately, cannot be calculated directly from surface observations. We assume that the horizontal component of the magnetic field is continuous across the core-mantle boundary, that the frozen-flux approximation adequately describes the time dependence of the horizontal component of the magnetic field at the core surface, and that most of this time dependence results from steady core motion. Then by treating the determination of the toroidal field at the core-mantle boundary as an inverse problem, we find that only very strong and spatially complex toroidal field models are consistent with both advection in the core and the decadal length of day variations. We argue that strong toroidal fields are necessary to account for the length-of-day variations since there is significant cancellation when the magnetic stress is integrated over the core-mantle boundary (CMB), the necessary time-dependent torque resulting from the slight and temporary noncancellation of magnetic stress established by a slowly varying and spatially complex toroidal field. But, since our toroidal field models are too strong according to dynamo theory, produce electric fields at the Earth’s surface which are stronger than measured values, and produce ohmic heating which either exceeds or contributes an unacceptably large fraction of the Earth’s surface heat flow, we deem the toroidal-field models consistent with our analysis of electromagnetic coupling to be physically unreasonable. Thus, we argue that core-mantle coupling is not predominantly electromagnetic. However, this conclusion may not hold if, for example,