Nonlinear Science, especially nonlinear dynamics in Hamiltonian systems for:
- Nonlinear optics - the dynamics of laser-cavity optics and telecommunication pulses in fibres.
- Fuid dynamics - the application of averaging, asymptotics and geometrical methods.
- Lagrangian-averaged Navier-Stokes-alpha models of turbulence.
Non-linear science, especially nonlinear dynamics - ranging from intergrable to chaotic behavoiur, from solutions to turbulence - in Hamiltonian systems for nonlinear optics and fluid dynamics. In nonlinear optics I am studying dynamics of laser-cavity optics and telecommunication pulses in fibres. In fluid dynamics I am applying averaging, asymptotics and geometrical methods from nonlinear dynamics, in deriving and analyzing models for computing high resolution global ocean circulation, including the effects of subgrid scales and turbulence on the Lagrangian mean motions. Recent work applies the Euler-Poincare theory to derive and analyze Lagrangian-averaged Navier-Stokes-aplha models of turbulence - an acitve area of my current study.