Ashley Willis

Dr.  Ashley P. Willis

Senior Lecturer of Applied Mathematics

Room H12, Hicks Building

School of Mathematics and Statistics
University of Sheffield
S3 7RH, U.K.

+44 (0)114 2223746


Office hours: Usually in my office, H12. To be sure, please email in advance.

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.


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:

Some of my work: