Tangential stress at the core–mantle interface

Abstract

SUMMARY Fluctuations in the rotation rate of the solid Earth over periods from 5 to 100 yr result from exchanges of angular momentum between the fluid outer core and the solid mantle. The coupling mechanism mediating angular momentum transfer is not clear yet. Here, I revisit local Cartesian models for the pressure stress on a bumpy core–mantle interface. One common approach consists in analysing forced magnetohydrodynamic modes arising from the interaction between a steady flow along the core–mantle interface and boundary topography. The wave amplitude scales as the height ζ of corrugations and the pressure stress as ζ2. As expected from Newton’s third law, the tangential stress on the fluid is opposite to the tangential stress on the solid. It is exactly compensated by non-zero mean electromagnetic and Coriolis forces, which both result from interactions at infinity and not with the electrically insulating solid. Requiring zero net flux of mass and electrical current at infinity in order to better model closed systems necessitates to restore mean flow acceleration. This makes possible to investigate whether there is momentum transfer into the fluid interior or instead dissipation next to the boundary. Fluid stratification enhances the horizontal stress exerted by the pressure field on the core–mantle boundary but we have yet to describe the mechanism to transport momentum from the boundary into the fluid.