Enhanced Core-Mantle Coupling Due to Stratification at the Top of the Core

Abstract

Fluctuations in the length of day (LOD) over periods of several decades are commonly attributed to exchanges of angular momentum between the mantle and the core. However, the forces that enable this exchange are less certain. Suggestions include the influence of pressure on boundary topography, electromagnetic forces associated with conducting material in the boundary region and gravitational forces due to mass anomalies in the mantle and the core. Each of these suggestions has strengths and weaknesses. Here we propose a new coupling mechanism that relies on the presence of stable stratification at the top of the core. Steady flow of the core over boundary topography promotes radial motion, but buoyancy forces due to stratification oppose this motion. Steep vertical gradients develop in the resulting fluid velocity, causing horizontal electromagnetic forces in the presence of a radial magnetic field. The associated pressure field exerts a net horizontal force on the boundary. We quantify this hybrid mechanism using a local Cartesian approximation of the core-mantle boundary and show that the resulting stresses are sufficient to account for the observed changes in LOD. A representative solution has \SI{52}{\meter} of topography with a wavelength of \SI{100}{\kilo\meter}. We specify the fluid stratification using a buoyancy frequency that is comparable to the rotation rate and adopt a radial magnetic field based on geodetic constraints. The average tangential stress is \SI{0.027}{\newton\per\meter\squared} for a background flow of $\bar{V}=\SI{0.5}{\milli\meter\per\second}$. Weak variations in the stress with velocity (i.e. $\bar V^{1/2})$ introduce nonlinearities into the angular momentum balance, which may generate diagnostic features in LOD observations.