Plesio-Geostrophy: A Rapid Dynamics Formulation for the Earth's Core

Abstract:

We have developed an approximation to the fluid dynamics of the Earth's core that is appropriate on short timescales (yearly to decadal). The need for this approximation, called Plesio-Geostrophy (PG), results from the fact that the physical regime of the core is so extreme as to preclude numerical solution of the full governing equations in their native form. An attractive alternative is to adopt the columnar approximation, sometimes called the quasi-geostrophic approximation, known to be appropriate in the presence of very rapid rotation on short timescales. In the presence of arbitrarily strong magnetic fields and buoyant forcing, we show how to develop a representation of the dynamics that involves axial averages of various magnetic and buoyancy-related quantities (each of which is a type of moment) and magnetic fields on control surfaces. The resulting equations are a set of 17 self-consistent partial differential equations, each in two-dimensions. We illustrate how the approximation can (i) capture the subset of 3-D inertial modes that have the simplest axial structure (absent magnetic and buoyancy forces) (ii) accurately describe the onset of convection (absent magnetic forces). The companion presentation by Holdenried et al describes the eigenmodes governed by rotation and magnetic fields. The representation holds the prospect of use in a data assimilation scheme that would be appropriate for treating data from ESA's Swarm mission together with observatory data and other satellite data from previous decades.