Control of inner core rotation by electromagnetic, gravitational and mechanical torques

Abstract

We compute the polar rotation of the Earth's inner core in response to the combined effects of electromagnetic, gravitational and mechanical torques. We obtain electromagnetic torques between 10 18 and 10 20 Nm, compared to gravitational torques between 10 19 and 10 21 Nm estimated by Xu et al. [Xu, S., Crossley D., Szeto, A.M.K., 1999. Variations in length of day and inner core differential rotation from gravitational coupling. Phys. Earth Planet. Inter., 116, 95–110] and Buffett [Buffett, B.A., 1996b. A mechanism for decade fluctuations in the length of day. Geophys. Res. Lett., 23, 3803–3806.], respectively. We obtain mechanical torques on the order of 10 15 Nm. Gravitationally dominated cases produce inner core oscillations with periods between 1 and 10 years. In electromagnetically dominated cases, the inner core rotates close to the imposed rotation rate of the outer core fluid. Modulations in the rotation rate are produced as the inner core passes through successive gravitational wells. These modulations occur over roughly 90 year timescales for outer core flow rates of 1°/year. When the electromagnetic torques are only marginally stronger than the gravitational torques, the inner core slowly rotates prograde by 90° relative to the mantle, escaping a gravitational well in roughly 100 years, then falls into the next gravitational well, rotating through 90° in just 4 years. Finite inner core viscosity is modeled using a relaxation time for the inner core topography. With relaxation, the gravitational torque reduces but does not eliminate the anomalous inner core rotation. Because of the short timescales of many of the irregularities in inner core rotation, it may be possible to observe them in presently-available seismic data.