ELECTROMAGNETIC COUPLING AND THE TOROIDAL MAGNETIC-FIELD AT THE CORE-MANTLE BOUNDARY

Owing to exchanges of angular momentum between the Earth's fluid outer core and the overlying solid mantle, the Earth's rotational rate fluc tuates on periods of a few years to a few decades. However, the mechan ism which allows the exchange of angular momentum is not understood. H ere we examine the possibility that core-mantle coupling is predominan tly electromagnetic and thus responsible for the decadal length of day variations. The electromagnetic couple on the mantle can be divided i nto poloidal and toroidal parts, and, by requiring continuity of the h orizontal component of the electric field at the core-mantle boundary, the toroidal couple can be divided into separate advective and leakag e parts. The poloidal couple results entirely from the interaction of the poloidal field with currents induced by its time variation; the ad vective couple results from the dragging of poloidal field lines throu gh a conducting mantle; and the leakage couple results from the diffus ion of toroidal magnetic field from the core's interior into the mantl e. The poloidal and advective couples can be estimated by using models of the downward continued poloidal field and models of the core veloc ity. We find that neither the poloidal couple nor the advective couple exhibit sufficient variability to account for the decadal length of d ay variations. If this is true, and if core-mantle coupling is indeed predominantly electromagnetic, then most of the variability in the len gth of day must result from the leakage couple, which, unfortunately, cannot be calculated directly from surface observations. We assume tha t the horizontal component of the magnetic field is continuous across the core-mantle boundary, that the frozen-flux approximation adequatel y describes the time dependence of the horizontal component of the mag netic field at the core surface, and that most of this time dependence results from steady core motion. Then by treating the determination o f the toroidal field at the core-mantle boundary as an inverse problem , we find that only very strong and spatially complex toroidal field m odels are consistent with both advection in the core and the decadal l ength of day variations. We argue that strong toroidal fields are nece ssary to account for the length-of-day variations since there is signi ficant cancellation when the magnetic stress is integrated over the co re-mantle boundary (CMB), the necessary time-dependent torque resultin g from the slight and temporary noncancellation of magnetic stress est ablished by a slowly varying and spatially complex toroidal field. But , since our toroidal field models are too strong according to dynamo t heory, produce electric fields at the Earth's surface which are strong er than measured values, and produce ohmic heating which either exceed s or contributes an unacceptably large fraction of the Earth's surface heat flow, we deem the toroidal-field models consistent with our anal ysis of electromagnetic coupling to be physically unreasonable. Thus, we argue that core-mantle coupling is not predominantly electromagneti c. However, this conclusion may not hold if, for example, core motion is highly time dependent, or if a strong diffusive boundary layer is p resent beneath the core-mantle boundary, the presence of which may all ow for a significant discontinuity in the horizontal component of the magnetic field and the breakdown of the frozen-flux approximation.