PhD Studentship: Multi-symplectic methods for nonlinear wave interactions and ocean wave forecasting

The motivation for this project is to develop the mathematical foundations for the next generation of ocean-wave forecasting models. Accurate and timely wave forecasts are essential for the safety of shipping, coastal communities, and offshore operations, including the construction and maintenance of offshore wind farms, wave-energy converter arrays, and other marine infrastructure. In particular, a principal objective of ocean-wave forecasting is to predict when and where extreme waves may occur, thereby helping to mitigate risks to lives, vessels, and offshore assets.  

Existing operational models (ECMWF’s ECWAM, NOAA’s WAVEWATCH III) are successful but are based on a weakly-nonlinear model for wave action conservation (kinetic equation). The mathematics now exists to take the theoretical and numerical underpinnings into the fully nonlinear regime. This project has two key aims: (a) develop a fully nonlinear kinetic equation using a multi-symplectic formulation, which will then serve as the backbone of the next generation ocean wave forecasting algorithm, and (b) develop new multi-symplectic numerical methods (structure-preserving algorithms in both space and time directions) for 2+1 Hamiltonian wave equations. These latter algorithms will then be used for both the forecasting model and an attendant fundamental study on nonlinear wave interactions and emergence of extremity and complexity in the theory of nonlinear waves and patterns. 

To choose one aspect that can be visualized: how is an extreme surface wave generated from nonlinear wave interactions? How does surface complexity arise from nonlinear water waves? This latter fundamental study will feed into the theory of forecasting.

Funded by: EPSRC Engineering and Physical Sciences Research Council 

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