Research Interests

Profile:
I am an applied mathematician working on various aspects of fluid mechanics, particularly related to interfacial and free-surface flows. I am interested in nonlinear differential equation problems arising in fluid mechanics, examining solutions using computational, asymptotic and dynamical systems methods.

Some of the particular research topics are in the following areas:

• Nonlinear interfacial waves with a free surface (EPSRC grant)
• Nonlinear hydroelastic waves in two and three dimensions (with Mark Blyth, Jean-Marc Vanden-Broeck, Philippe Guyenne).
• Hydroelastic waves and their interactions with vertical cylinders (in collaboration with Alexander Korobkin and Paul Brocklehurst)
• Linear and nonlinear waves in elastic pipes and channels (with Neil Deacon, Richard Purvis and Robert Whittaker)
• Computations of solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem (in collaboration with Jean-Marc Vanden-Broeck and Mark Cooker).
• Modelling the behaviour of colloidal suspensions (in collaboration with Carl Roberts, Mark Cooker, Rob Penfold, Richard Purvis)
• Nolinear waves generated by a moving load on top of an ice plate; dynamical system approach and forced nonlinear Schrodinger equation (in collaboration with Frederic Dias)
• Generalised interfacial solitary waves (in collaboration with Frederic Dias)
• Modeling of tha trajectory and breakup of spiralling liquid jets (in collaboration with Stephen Decent, Mark Simmons, A. C. King)
• Fixed points theorems in probabilistic metric spaces (in collaboration with V. Radu)

Potential Ph.D projects are available in the area of internal waves in the presence of a free surface (see Internal waves with a free surface) and three-dimensional nonlinear hydroelastic waves. They will involve analytical and numerical work.