On the theory of core-mantle coupling

Abstract

This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the associated gravitational oscillations, is presented. Magnetic coupling through torsional waves is studied. A fresh analysis of torsional waves identifies new terms previously overlooked. The magnetic boundary layer on the core-mantle boundary is studied and shown to attenuate the waves significantly. It also hosts relatively high speed flows that influence the angular momentum budget. The magnetic coupling of the solid core to fluid in the tangent cylinder is investigated. Four technical appendices derive, and present solutions of, the torsional wave equation, analyze the associated magnetic boundary layers at the top and bottom of the fluid core, and consider gravitational and magnetic coupling from a more general standpoint. A fifth presents a simple model of the adiabatic reference state.