2018- : Senior Lecturer, School of Mathematics & Statistics, University of Sheffield, U.K.
2010-17 : Lecturer, School of Mathematics & Statistics, University of Sheffield, U.K.
2008-10 : EU Marie Curie Fellow (PI), Laboratoire d'Hydrodynamique (LadHyX), Ecole Polytechnique, Paris, France
2005-08 : EPSRC Research Associate, School of Mathematics, University of Bristol, U.K.
2002-05 : NERC Research Fellow (RA), School of Earth Sciences, University of Leeds, U.K.
2002     : PhD Applied Mathematics, Newcastle University, U.K.

Research

Pattern formation in fluid flows (transition to turbulence, nonlinear dynamics, stability, chaos). Astrophysical fluid dynamics and magnetohydrodynamics (flows in planetary interiors, accretion discs, magnetic field generation).

Google Scholar page for APW

School page for APW

PhD Projects

The modelling of fluid flows is perhaps the traditional test-bed for the development of new mathematical methods, and there are many applications involving fluids in the area of clean energy, such as thermal exchangers in solar and geothermal systems, and in wind and wave energy capture. Turbulent flow is characterised by chaotic whirls or eddies, which effectively enhance diffusion and dissipate kinetic energy. This might aid mixing or heat transfer, but dramatically increases the cost of pumping fluids. Therefore, understanding how and when turbulence appears is typically crucial in applications. On a larger length scale, astrophysical applications include the dynamics of flows inside planets and proto-planetary flows about a central mass (accretion discs). Magnetic fields typically play an important role in determining the nature of these astrophysical flows.

I am looking for motivated students who would like to apply and broaden their mathematical skills. I expect you to be familiar with differential equations and vector calculus; you do not need to have taken advanced courses on fluids. For further information please contact me. Please note that all PhD applications must be made through the university system: PhDs: How to apply.

Project examples:

• Transition to chaotic or turbulent flow can linked to solutions of the Navier-Stokes equations, but which solutions are important, and how can we improve methods to calculate them? The solutions we have found so far typically only capture eddies of a single length scale.. how can we find solutions that capture the multi-scale nature of turbulence? Single-scale examples for the flow through a pipe can be seen here.

• Can we use optimisation to reduce energy expenditure? For example, experiments have shown that, surprisingly, introducing a partial blockage in a pipe can eliminate turbulence, rather than just stirring the flow up to produce more turbulence. This makes pumping the fluid a lot easier downstream of the blockage, but pumping fluid past the blockage itself it is more expensive. Can we create this effect by less expensive means? Can we find an 'optimal' strategy?

• Some planets, like Earth, have a magnetic field, others do not. Typically the magnetic field is produced through the motion of electrically conducting fluid, like liquid iron in Earth's core. But what properties of the flow are essential for magnetic field growth? In this article I found the optimal flow for magnetic field growth (and minimal magnetic Reynolds number), but what is it about this flow that is so special? What happens under more realistic constraints on the flow, such as the geometry of the boundaries, e.g. within in a sphere or spherical shell?

• Observations of astrophysical flows around a central body (accretion discs) suggest that these flows are turbulent, while mathematically the flows should be linearly stable. So is there a nonlinear instability mechanism? If so, it occurs at too large flow rate to compute directly in simulation; astrophysical flow rates are huge. Can we develop a reduced model that captures the essential physics to investigate this nonlinear dynamics?