The dynamics of jets in rapidly rotating fluids by computational fluid dynamics (CFD) simulation (EPSRC DTP)

Supervisor(s)

Dr Phil Livermore, Professor Rainer Hollerbach, and Professor Chris Finlay

Contact Dr Phil Livermore (P.W.Livermore@leeds.ac.uk) to discuss this project further informally.

Project description

The movement of electrically conducting liquid inside the core of Earth and other planets is responsible for generating their planetary magnetic fields, yet we know very little about their dynamics, as creating realistic simulations is extremely challenging.

This project is focused on creating a new type of numerical model for rotating planetary cores, which uses techniques used extensively elsewhere in fluid dynamics: computational fluid dynamics. Such techniques offer a novel method to study local phenomena such as jets within planetary cores.

Of particular relevance for this project is the recent discovery by the supervisory team of a jet within Earth’s core at high latitude, using the latest satellite data. This jet is believed to arise due to the influence of rapid rotation on the movement of the fluid within planetary cores, aligning the flow into structures parallel to the rotation axis.

Important dynamics may occur if there is a solid inner core – as there is inside the Earth - dividing the fluid into disconnected regions, because the fluid’s response is to form a jet on the interface. This jet may play an important role in the global dynamics of the Earth’s core (just as the jet-stream does in our atmosphere) and also may act to excite torsional waves, which travel within the core and are magnetically observable.

Although the jet is described by a simplistic theoretical framework, there is currently no numerical model that can simulate its existence or time-dependent dynamics. Most models of the Earth’s core are spherical, and focus on the broad global dynamics. However, in this project, spanning both geophysics and applied mathematics, we will focus attention at the local region at high latitude, investigating how jets and other structures form, and their expected signature within the magnetic field.

The work will involve developing new theory and using numerical high-resolution computational fluid dynamics (CFD) supercomputer models of rapidly rotating fluids using both the Nek 5000 software package that is based on spectral elements, and OpenFOAM that is based on finite volumes.

The student will learn the theory of fluids within the Earth’s core, but also how to use CFD packages to produce images and animations.

Project objectives:

1. To model the dynamics within the electrically-conducting fluid of Earth’s core at high-latitude, investigating jet and other flow structures and how they evolve.

2. To investigate whether a jet can, through electromagnetic coupling, cause the solid inner core to rotate. To identify any waves caused by high-latitude jets.

3. To compare the magnetic signature of the jet and waves, to the observations from high-resolution satellite measurements of the Earth’s magnetic field.

Project timeline:

Year 1: To use the NEK5000 and OpenFOAM CFD packages to model the hydrodynamics (non-magnetic) of a rotating fluid cylinder (as an approximation to the tangent cylinder) containing a horizontal solid disk (modelling the solid inner core). Production of high-quality animations showing, for example, a simulation of the Taylor-Proudman theorem (the movement of the fluid as columnar structures). Investigation of the extension of this model setup to electrically-conducting fluids, and motion with a prescribed background magnetic field whose structure triggers a jet to form.

Year 2: The simulation of dynamics within the northern high-latitude region of Earth’s core, by modelling a cylindrical sub-volume from the spherical core that includes the tangent cylinder. By choosing appropriate background magnetic fields, model the development and evolution of jets and other rapidly evolving structures. Comparison of the jet’s magnetic signature to satellite-observation-derived models of the geomagnetic field.

Year 3: By allowing the solid inner core to freely rotate within the model, investigate whether a jet, through electromagnetic coupling, can cause the inner core to rotate. Identification of any waves (e.g. torsional or magnetic Rossby waves) caused by the jet and their observational signature within the magnetic field. Comparison of wave motion to satellite observations.

Training: The student will learn both the theory and computational techniques required to model the dynamics of the electrically-conducting fluid of the Earth’s core, and will have access to a broad spectrum of training workshops put on by the Faculty that include an extensive range of workshops in numerical modelling, high-performance computing, through to managing your degree, to preparing for your viva.

The student will be a part of the deep Earth research group, a vibrant part of the School of Mathematics and the Institute of Geophysics and Tectonics, comprising staff members, postdocs and PhD students. The deep Earth group has a strong portfolio of international collaborators which the student will benefit from. Although the project will be based at Leeds, there will be opportunities to attend international conferences (UK, Europe, US and elsewhere), and collaborative visits within Europe.

Entry requirements

We seek a highly motivated candidate with a strong background in mathematics, physics, computation, geophysics or another highly numerate discipline. The minimum requirement is British Bachelor's 2.1 (or equivalent) or Master's degree.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website.

If you require any further information, please contact the Graduate School Office e: apply-phd@see.leeds.ac.uk, or t: +44 (0)113 343 1634.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.