Tidal despinning of the mantle, inner core superrotation, and outer core effective viscosity

Abstract

Dissipation of tidal energy in the oceans causes a net transfer of angular momentum from the spin of the Earth to the relative orbital motions of the Moon and Sun. These torques couple directly to the mantle, and cause it to despin. Viscous coupling across the outer core is an effective means of communicating this change to the inner core. The Ekman time scale for dissipation of transient fluid motions associated with unsteady torques is much shorter than the time scale for adjustment of inner core and mantle rotational velocities in the steady Couette flow regime. The relative amplitude and phase of rotational variations in this system, with respect to the applied torques, are given in terms of core viscosity and torque variation frequency. Any short period variations in mantle torques will leave the inner core largely unchanged, and the influence of long period and secular torques applied to the mantle is efficiently transmitted to the inner core. The system response to a steady tidal torque applied to the mantle leaves the inner core with a small excess rotational velocity relative to the mantle, proportional to the product of outer core viscosity and the applied mantle torque. Recent estimates of an inner core super‐rotation of ˜1 degree/year imply an effective outer core viscosity of ˜103 Pa s. Glacial cycle variations in tidal torques somewhat complicate this picture, but do not yield significantly different viscosity estimates. However, they do imply that the differential rotation velocity varies by roughly a factor of 2 over a 100 kyr glacial cycle. The tidal shear strain may also contribute to development of anisotropy in the inner core.