Magnetostrophic analysis of Earth's internal magnetic field

Throughout this thesis we build on the central tenet of the seminal work by Taylor (1963), which argued that the geophysically relevant limit for dynamo action within the Earth's outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this 'magnetostrophic' limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed 'Taylor states'.

We extend the use of this condition, to analyse the geomagnetic field and investigate the underlying geodynamo process within Earth's core, through several key strands of work.

Firstly, we detail a general method that is the first to enable correct evaluation of the instantaneous geostrophic flow for any 3D Taylor state, fully incorporating all necessary boundary conditions.

Secondly, we explore the subsequent dynamics of Taylor state magnetic fields, calculating the field induced by these flows and hence the rate of change of magnetic field. Importantly, we note the similarities and differences that arise between these magnetostrophic dynamo models and observationally derived geomagnetic field models. We show that Taylor state magnetic fields that remain stable over geophysical time scales are very rare.

Thirdly, we consider the prospect of the fluid in the outermost part of Earth's core being stratified. This leads to a necessary adaptation to the Taylor constraint, resulting in the analogous condition within a stratified fluid, termed the 'Malkus constraint'. Implementing this additional constraint allows us to construct a model for the entirety of Earth's outer core, matching observational geomagnetic field models at the core surface, obeying the Malkus constraint in the stratified layer and satisfying the Taylor constraint in the bulk of the core.
The results from this model suggest that the dynamics within the stratified layer may be distinct from the inner convective part of the core, characterised not only by suppressed radial flow but by a strong magnetic field. The present-day toroidal field strength immediately beneath the CMB is estimated to be significantly stronger than that within the convective region of the outer core.