Cross Disciplinary Models of Polar Convection in Earth's Core

Abstract:

The large scale magnetic fields of terrestrial planets are maintained by turbulent convection in their deep interior. Direct measurements of the convection are not possible and the primary tool for investigating the underlying dynamics is numerical simulation of the MHD equations in a (global) spherical shell rotating about the vertical axis. The leading order force balance in these simulations is typically geostrophic (a balance between the Coriolis and pressure gradient forces) with magnetic effects entering at next order. This motivates the study of rapidly rotating hydrodynamic convection as an analogue system of planetary interiors.

Alongside global simulations, models of the polar region have been developed for which gravity is aligned with the rotation axis; laboratory convection experiments consider cylindrical geometries and simulations consider an infinite plane layer. Convection systems are often characterised by the Nusselt number, $Nu$, which measures the convective heat transport. At the same values of the input parameters, both the actual values of $Nu$ and the scaling behaviour differ significantly between local and global models.

Here we bring together the results of three synergistic studies of rapidly rotating core-style convection: laboratory experiments, plane layer simulations, and a cylindrical domain harvested from the polar region of our global simulations. We show that for rapidly rotating convection (Ekman number, $3e-6<E<5e-5$), the laboratory and plane layer models are in excellent agreement with the polar region of global simulations in terms of both heat ($Nu$) and momentum ($Re$) transport. Crucially, then, this study provides the first demonstration that zeroth order quantitative agreement exists between differing end-member models of planetary core dynamics.