Building a realistic model of Earth's magnetic field using constrained dynamics

A proper understanding of how the geomagnetic field is generated in Earth’s liquid core, by the so-called geodynamo, remains one of the greatest outstanding problems in Earth science. The principal difficulty is that the core is far too remote to be probed directly and that observations from Earth’s surface can only constrain the magnetic field at the edge of the core.

From a mathematical standpoint, on medium to long time scales, the core can be realistically modelled as a constrained dynamical system. Such an idea may be more familiar from classical mechanics, where it is used to model a pendulum, rod assemblies and (industrial) robots.

The focus of this project is to consider the Earth's core as evolving under the control of constraints, called the Taylor constraints, which stem from the dominance of the rotational forces. In addition, recent evidence suggests that the outermost part of the core is stratified, leading to a further set of Malkus constraints. The goal is to construct both static and dynamical models of the magnetic field that satisfy this large set of constraints. Ultimately, this may shed light on fundamental features which are still unexplained, such as why the field is predominantly aligned with the rotation axis, and how the magnetic field undergoes global reversals.