The magnetohydrodynamical modes of plesio-geostrophy

Abstract:

In recent decades, the availability of brand-new satellite data has paved the way for studies of the Earth's secular variation. In particular, core-flow inversions which encode a-priori the axial rigidity conferred to flows on short time scales by the Earth's rapid rotation have shed new light on fast dynamics, and provided new estimates of the magnetic field strength inside the core. A new formalism, plesio-geostrophy (PG), also presented in this session, aims to provide an improved description of core dynamics which may be used for geomagnetic data assimilation.

We consider the diffusionless, inviscid dynamics of a fluid in a full sphere subject to a magnetic field under the PG paradigm. The action of Coriolis and Lorentz forces can sustain two types of eigenmodes which are a subset of 3D magneto-inertial eigenmodes and whose frequencies define fast and slow branches. The behaviour of these modes is characterised against azimuthal wavenumber and Lehnert number, the latter quantifying the strength of magnetic to inertial forces. In the regime of small Lehnert number (< 10^-2), we show that these modes can provide a good description of full 3D modes, capturing their essential features. These results suggest that PG should provide a sound basis for geomagnetic data assimilation.