Stochastic wave modelling for inhomogeneous sea-states

This project aims to improve modern wave forecasts by developing a better understanding of the nonlinear interaction of random surface water waves. While the simplest mathematical models of waves are linear, and assume that waves of different frequencies do not interact, a more detailed understanding of the sea must take into account departures from linearity. In the deep waters of the open sea, where waves are generated by the action of the wind, the fundamental nonlinear energy exchange occurs between quartets of four waves.These energy exchanges, together wave-breaking and wind, are the main inputs into wave-forecasting models. Such models inform the surfer waiting for a big swell as well as the engineer planning offshore operations - by providing an accurate and timely forecast of wave conditions. Moreover, equations describing the evolution of the sea-state can be used to predict the likelihood of anomalously high rogue waves, which have been implicated in shipping accidents since antiquity.Current modelling relies on equations that assume waves to be uncorrelated - implying that the sea is spatially homogeneous. This classically results in an equation with a very long evolution time-scale, and excludes phenomena of physical and mathematical interest. This project is devoted to studying how correlation between wave modes impacts the evolution of wave fields, and to developing novel equations that can be implemented in wave forecasting systems.