A comparison between the magnetohydrodynamical modes of plesio-geostrophy and fully 3D calculations

An ever-expanding catalogue of satellite data has laid the foundations for new studies of Earth’s secular variation and acceleration. Studies that encode a-priori the axial rigidity conferred to core flows by the Earth’s rapid rotation have revealed novel fast dynamics and improved estimates for the magnetic field strength inside the core. Within this context, a new formalism christened “plesio-geostrophy” (PG) was developed by Jackson and Maffei (Proc. Roy. Soc. A, 476(2243), 2020) with the purpose of describing core dynamics in a regime closer to Earth's conditions. This model makes use of axial integration of the equations of fluid motion and magnetic induction to collapse all three-dimensional quantities into two-dimensional scalars. We report on new results within the PG formalism.

We consider the dynamics of a conducting, inviscid fluid in a full sphere subject to various background magnetic fields. The eigenmodes sustained by the Coriolis and Lorentz forces split into two branches: a fast and a slow one. We characterise these eigenmodes and compare their structure and frequency to fully three-dimensional results. Previous studies are extended by incorporating the effects of horizontal magnetic diffusion.