Nonlinear wave patterns
Check out our current research projects in nonlinear wave patterns.
Wave fronts and nonlinear patterns (phase dynamics and Whitham modulation theory)
Whitham modulation theory and its generalisations. Deriving new universal model equations and applying them to water waves. Recent work led by Tom Bridges involves deriving a generalised two-way Boussinesq equation to model the Benjamin-Feir instability transition in shallow water hydrodynamics.
David Lloyd and Matthew Turner are investigating the range of localised cellular structures in binary fluid convection using radial centre-manifold techniques. The local centre-manifold reduction has been shown to work by identifying localised spots and rings in the ferro-fluid problem by Hill, Lloyd, and Turner (2021, J. Nonlinear Sci.). This problem was essentially two-dimensional as the localised structures formed on the surface of the fluid. The binary convection problem is a step into extending these ideas into three-dimensions.