Nonlinear wave patterns

Check out our current research projects in nonlinear wave patterns.

Research leads

Thomas Bridges profile image

Professor Tom Bridges

Professor in Geometric Mechanics and Lagrangian Fluid Dynamics

David Lloyd profile image

Professor David Lloyd

Professor in Localised Pattern Formation and Mathematical Modelling

Wave fronts and nonlinear patterns (phase dynamics and Whitham modulation theory)

Sea wave starting to crash

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.

Nonlinear patterns

Ferrofluid close-up

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.

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