Geomagnetic Westward Drift Precludes Inner Core Differential Rotation

Abstract:

The geomagnetic westward drift and the inner core differential rotation are two components of the Earth’s core rotational dynamics. We present a systematic study of their long-term relationship in convective numerical simulations of the geodynamo. All models comprise gravitational coupling between the inner core and the mantle, in addition to electromagnetic coupling at the inner core and core-mantle boundaries. We show that the strength of these couplings has no influence on the global shear available in the fluid shell, whose amount is entirely governed by the vigor of convection. This shear is distributed between the long-term westward drift and the long-term differential rotation of the inner core, in proportions controlled by the magnitudes of the electromagnetic and gravitational couplings. Present-day estimate of this available shear matches the westward drift observed on average during the last 400 years, which implies a non-existent long-term inner core differential rotation. Assuming a lower mantle conductance of order 10⁸ S, this in turns sets a constraint on the minimum stiffness of the inner core, the viscosity of which should be larger than 2×10¹⁷ Pa.s for the westward drift to dominate.