Publications
You can find my recent publications through the Research Explorer.
Current research projects and interests
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Stratified fluid dynamics. Particularly internal waves and
nonlinear wave phenomena.
Numerical methods for fluid dynamics.
Non-Newtonian fluids. Flows through porous media.
Applications of machine learning algorithms, particularly to
image-like data.
Image analysis. Modelling change in image sequences.
Sub-sampling methods for big data.
Current research students
Currently I am co-supervising a PhD student, Johannes Hansen, jointly with Edward Mitchard. Johannes is working on models for detecting change in SAR satellite imagery with the purpose of improving the detection of deforestation. The project is co-funded by Datalab, and has the involvement of Ecometrica as an industrial partner.
Past research
A dense gravity current
My research interests have encompassed a range of problems within applied mathematics. I am particularly interested in fluid dynamical phenomena. Within fluid dynamics my past research has principally been on inviscid stratified flows, however I also have interests ranging from Stokes' flow to non-Newtonian fluids.
Viscous fluid flow under gravity through a leaky fracture
I began my research career studying flow through porous rock, and in particular flow through fractured rock. During my Masters thesis I worked on the flow of a gravity current of non-Newtonian fluid through a model fracture. After this in my PhD thesis I examined a range of viscous flows through leaky fractures. These flows modelled the spreading and slumping of a viscous fluid through a fracture adjacent to a porous layer, so that some fluid was lost to the layer from the fracture. These studies were done with a combination of experimental and analytical techniques. I also examined the problem of a viscous gravity current dipole flow through a channel. Some of the experimental photographs from this work can be seen below and right. More recently I have returned to flows through porous media and have become interested in non-Newtonian flows, particularly with a view to developing new numerical models for these.
Viscous dipole flow through a channel
The more recent focus of my research has been to develop and construct advanced numerical models for stratified flows. This has been joint work with David Dritschel, with whom I have developed a range of numerical schemes for dealing with such flows using contour based methods. David has a long history of developing and exploiting advanced computational techniques using contour methods, and we have been engaged in updating and extending the code base that he has developed over the years. This has led to a suite of codes applicable in a range of areas, including spherical shallow water models, stratified flows, quasi-Geostrophic flow and others.
Exhange flow
I am also particularly interested in internal solitary waves (ISWs), and their behaviour as they break. Such waves are supported across the pycnocline in the ocean and when they break can result in a significant amount of mixing. As part of a project working with Magda Carr as a PDRA I was able to visit the University of Oslo together with a PhD student James Franklin, to conduct some experiments with colleagues there in their large flume tank. Subsequently we have compared these measurements with numerical models of breaking ISWs.
A breaking internal solitary wave