My research interests are in mathematically modelling environmental phenomena. Very often such naturally occurring flows are two-phase; they feature both solid particles and fluid. Large-scale examples include avalanches of rocks and snow, volcanic ash clouds, landslides, debris and mud flows, and the erosion and transport of sediment in coastal environments. Modelling these flows requires the development of physically-relevant mathematical models and the computation of their solutions using analytical and numerical techniques. Much of the research is interdisciplinary, with colleagues from the departments of earth science and engineering in Bristol and beyond.

Ph.D. Projects

Below I describe some current projects and interests, but this list is not exhaustive and continually evolves. I am happy to discuss other potential project by e-mail. Please see my web pages for recent publications.

1. Volcanic ash flows in the atmosphere
   Flows of volcanic ash are driven by the presence of suspended particles, which render the suspension denser than the surrounding fluid and this buoyancy difference drives the dispersion of the particle-laden cloud. The particles, however, continually settle out of the suspension, thus progressively reducing the excess density of the cloud and the speed of the flow. Volcanic ash clouds are also advected by atmospheric conditions and wind plays a major role in their dispersion.
   
   The 2010 eruption of Eyjafjallajokull in Iceland, which although relatively small for volcanic eruptions, caused very substantial disruption to air travel across western and northern Europe. The inability to predict the motion of the ash cloud with any accuracy became clear during this period; current models do not properly account for the motion of cloud through the atmosphere and its interaction with wind. These deficiencies will be addressed by this research to model the rise of the ash-laden volcanic plume through the atmosphere and its mixing with it, and the intrusion of the volcanic cloud through the atmosphere and its dispersion by the wind. The work could entail mathematical modelling, computation or laboratory experimentation on small-scale flows that share many features with these important environmental phenomena.
   
   (See \url{www.plumerise.bris.ac.uk} for an implementation of a model of volcanic plume rise though a stratified, windy atmosphere.)
   
   
2. Granular segregation
   
   Mixtures of particle with different sizes and densities tend not to remain uniformly mixed when flowing. For example, in an agitated mixture of particles, the smaller ones tend to migrate towards the bottom, a phenomenon which causes problems in industrial processing and which plays a major role in determining the deposit from large-scale flows of particles in the environment. However despite its inevitability, quantitative models of segregation remain in their infancy and we cannot predict the rate of segregation of a mixture of particle sizes with any certainty. This project would address this issue by developing new models to capture recent experimental measurements of granular segregation, by developing simulations of the process in particular flows and by calculating the deposit that would be left behind by such motions.
   
   
3. Suspended sediment transport
   
   River currents and coastal waves may pick up sedimentary particles if their flow is sufficiently intense. Thereafter the particles are carried along in suspension with their submerged weight being supported by the action of fluid turbulence. It is important to be able to predict the quantity of sediment that a flow may transport so that accurate assessment may be made of the rates of coastal erosion or the effects of building new engineering structures, such as barrages and harbours on the surrounding environment. The current formulae for predicting this erosion are highly inaccurate and estimates may be incorrect by orders of magnitude. This Ph.D. project will adopt a new approach to modelling suspended sediment transport. It will employ recent ideas from studies of turbulent fluid flows in which coherent eddies and other flow structures have been identified. These structures are potent means for transporting sediment in suspension and this project will examine how models involving these flows may significantly improve our understanding and ability to quantify the amount of particulate material that may be transported.
   
   
4. Flows of mud, debris and viscoplastic materials
   
   When a fluid is highly laden with particles or contains a significant fraction of mud, it may exhibit dynamical features that differ strongly from situations in which the particulate phase is dilute. Most notably the fluid may exhibit a yield strength that must be overcome for motion to occur. Below this yield stress the material behaves like a solid, whereas above it, it flows like a fluid. Fluids with this property are termed viscoplastics and as well as occurring in environmental settings, they are common in industrial processes, in particular oil drilling and food manufacturing. The transition between solid-like and fluid-like behavior leads to complex behavior in even simple flow regimes. For example, environmental mud flows may abruptly arrest or form channelised and braided streams. Recent experiments and field observations have highlighted a number of these features and Ph.D. projects in this area would develop quantitative, mathematical models of the flows of these materials.