Nonlinear Waves and Geometric Fluid Dynamics Group

Fluid dynamics is the study of fluid motion (liquids, gases, and plasmas) and the forces exerted by the fluid on its surrounding.


Our group uses mathematical techniques such as asymptotic methods, reduced model analysis and numerical modelling to investigate fluid flows. We also use more geometric techniques such as geometric mechanics along with other geometries including differential, symplectic, Kähler, algebraic and discrete in order to describe various features of different flow systems.


Our themes range from fluid stability problems and vortex modelling on both small and large scales to the study of conservation laws and geodesic flows. Fluid dynamics applications of these research themes include predicting weather and climate systems, modelling turbulence, investigating fluid transport problems, modelling complex fluid flows and plasma modelling.

Further geometric mechanics applications are to the stability, bifurcations, dynamics and numerics of Lagrangian and Hamiltonian ODEs and PDEs, to non-Hamiltonian perturbations.

Our group includes academics who are involved in cross-disciplinary research projects such as environmental fluid flows (with the Centre for Environment and Sustainability) and data assimilation in weather prediction (with the National Centre for Earth Observation), modelling open quantum systems (with the Quantum Foundation Centre) and modelling wave fronts in crime data (with the Centre for Criminology).

Research areas

Our research areas include:

  • Geometric mechanics
  • Geophysical fluid dynamics
  • Hydrodynamic stability
  • Water waves
  • Wave fronts and nonlinear patterns.

Research applications

The applications of our research include the following:

  • Complex fluids (Tronci)
  • Data assimilation (Lloyd, Santitissadeekorn)
  • Fluid transport (Bridges, Turner)
  • Multiscale analysis (Cheng)
  • Nonlinear patterns (Lloyd, Turner)
  • Plasma modelling (Tronci)
  • Turbulence (Turner)
  • Wave energy extraction (Bridges, Turner)
  • Weather and climate modelling (Cheng, Roulstone).

Join us

Fees and funding

There are plenty of funding sources available through various agencies.

PhD applications

We are currently accepting PhD applications. Take a look at our mathematics, nonlinear waves and geometric fluid dynamics studentship.


Take a look at our upcoming seminars.

Contact us

Find us

Department of Mathematics
Thomas Telford building (AA), floor 4
University of Surrey