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; scientific knowledge has advanced through exploiting the limited set of observations and computer simulations of the Earth’s core. The computational models, much like those used to simulate weather or climate, have improved significantly in the last few decades, largely due to the ongoing technological improvements in computing.
From a mathematical standpoint, on medium to long time scales, the core can be realistically modeled as a constrained dynamical system. Such an idea may be more familiar in mechanical systems such as (industrial) robots, which are often modeled as constrained dynamical systems: the parts move under the force exerted by motors according to the laws of mechanics under the constraint that the rods and other elements do not extend or compress. The rods in such systems can also be considered as springs in the limit that the stiffness constant goes to infinity. Specialized numerical methods are required when simulating such systems.
The idea of this project is to consider the Earth's core as evolving under the control of a system of constraints, called the Taylor constraints. The existing numerical methods will need to be adapted to this setting, in which the underlying dynamics are described by partial differential equations, now subject to a continuous family of constraints.
Realistic models of the long term operation of the geodynamo, the mechanism responsible for generating Earth’s magnetic field, may shed light on several macroscopic features of the field which are still unexplained. The first is the fact that the Earth’s field is predominantly aligned with the rotation axis; the second are global magnetic reversals which occur, on average, a few times every million years.
This project will involve both theoretical and computational aspects in modeling the Earth’s geodynamo as a constrained dynamical system. The student will begin by formulating the equations of motion and the structure of the constraints. Existing code will be modified and adapted to encode the mathematical model, which will be run on the Leeds university supercomputer ARC2.
The student will learn both the theory and computational techniques required to model the Earth’s core. Training in programming and running code on massively parallel supercomputers will be given. The student will be housed in applied mathematics, but will be a part of the deep Earth research group, a vibrant and active group that spans the Institute of Geophysics and Tectonics and applied mathematics. The deep Earth group has a strong portfolio of international collaborators from which the student will benefit. Although the project will be based at Leeds, there will be opportunities to attend international conferences (UK, Europe, US and elsewhere), and potentially collaborative visits within Europe.
We seek a highly motivated candidate with a strong background in mathematics, physics, computation, geophysics or another highly numerate discipline. Knowledge of geomagnetism is not required, and training will be given in all aspects of the PhD.
For further information please contact Jitse Niesen ([email protected]
) or Phil Livermore ([email protected]
How to apply - please visit: http://www.maths.leeds.ac.uk/postgraduate-research.html
Further reading / bibliography
A Millennium of Geomagnetism, online material: http://www.phy6.org/earthmag/mill_1.htm
A three-dimensional self-consistent computer simulation of a geomagnetic field reversal, Glatzmaier & Roberts, Nature 377, 203-209, 1995.
The evolution of a magnetic field subject to Taylor’s constraint using a projection operator, Livermore et al., 2011.
Numerical methods in multi-body dynamics, Eich-Soellner & Führer, Teubner Stuttgart, 1998.