Variations in length of day and inner core differential rotation from gravitational coupling

Abstract

Gravitational coupling between the inner core (IC) and mantle exchanges angular momentum between them and causes variations in the length of day (LOD) and the IC differential rotation. We simulate the coupled rotation of a triaxial ellipsoidal Earth — IC, outer core (OC) and mantle — using gravitational and pressure coupling torques and integrate the angular momentum equations in the time domain. The IC differential rotation is found directly from the resulting time series, whereas LOD oscillations are determined from a spectral analysis of the mantle rotation. The LOD oscillation period depends on the choice of triaxiality model for the IC, and varies between 4 and 18 years. We show that a previous formulation of this problem, in which the IC rotates about a fixed axis, is a special case of the present approach which adopts a general rotation allowing both axial rotation and wobble-nutation motions. The differences in the IC gravitational torque between the two formulations are that there is only one torque term in the simple rotation while there are two terms (called p-related and q-related torques) in the general rotation. It is found that the q-related torque corresponds to that in the case of simple rotation, and the p-related torque can be larger than the q-related torque. We also find that a differential rotation of the IC with respect to the mantle, caused by the gravitational torque, is controlled by the IC obliquity. Although it is unlikely that the gravitational torque alone creates a super rotation similar to that reported from some of the recent seismic observations, the gravitational torque effect should probably not be neglected. A few degrees in the IC obliquity produces an IC differential rotation larger than that suggested by seismology, implying that the figure axis of the IC probably deviates from that of the mantle by less than 1°. If that is correct, it may suggest that the IC anisotropy axis is not aligned with the IC figure axis (a difficult and unresolved issue), since it is observed from conventional seismology that the former deviates from the earth's rotation axis by 5–10°. One of the advantages of our time domain approach is that the problems of LOD, IC differential rotation, and wobble-nutation can be investigated consistently. Triaxiality of the earth (in particular, the IC) is necessary to produce axial gravitational torques between the IC and mantle, and hence LOD variations and IC differential rotation, but triaxiality does not change the periods of wobble-nutation modes obtained in previous studies for small obliquities ≪1°.