Viscous and Magnetic Boundary Layers at the Top of the Core in Geodynamo Models

We investigate the boundary layer at the top of the Earth’s core, which acts as a filter between the interior of the core and its surface, where models built from geomagnetic data are derived. We rely on no-slip convective geodynamo numerical simulations calculated for a low viscosity fluid, with Ekman numbers E=10-6 and E = 10-7, and an electrically insulating mantle. Magnetic diffusion is weak in the interior, where its contribution to the field changes varies inversely with the magnetic Reynolds number. From an analysis of the velocity and magnetic field radial profiles, we clearly identify a boundary layer region. This consists of a thick magnetic diffusive layer encompassing a thin Ekman-Hartmann viscous sublayer mainly affecting the velocity field. Taking the interior velocity as toroidal, a local theory for the viscous layer accounts well for the global numerical results. It yields better predictions when applied assuming only the large scale part of the radial magnetic field permeating the viscous layer. In contrast with predictions of the local theory, the thickness of the magnetic diffusive layer appears to be independent of the length scale along the core-mantle boundary. The flow vorticity varies abruptly next to the rim of the cylindrical surface tangent to the inner core. This entails Ekman pumping into the viscous layer, which yields localized induction of radial magnetic field. This mechanism is emphasized in the low Ekman, E = 10-7, simulations.