Towards modelling wave height probability distributions of "averaged" and "transient" sea states from first principles

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Wind waves in seas are inherently random. Despite the progress of engineering, unpredicted extreme waves in the ocean remain a serious danger for ships and offshore structures. In recent years there was a number of accidents with large ships resulting in loss of life and pollution of large sea and coastal areas. The UK, as an island trading nation, increasingly depends on ever expanding shipping and offshore activities. The loss of life, disruption (even temporary) of supply lines or of offshore energy production have become totally (morally and economically) unacceptable. To address these challenges thorough understanding of random sea waves is needed, first of all, knowledge of the dependence of their probability distribution on wave interaction with atmosphere. In the situation of changing weather patterns the required knowledge of, say, a "100-year wave" for a particular place cannot be obtained from past experimental records, and a comprehensive theoretical model deduced from first principles is needed. Now a radical improvement compared to the present state of affairs has become possible. This is the aim of the proposed project.At present all wave forecasting and modelling, which is a part of routine meteorological forecasting, is based on the numerical integration of the kinetic (Hasselmann) equation. The equation derived from first principles takes into account wind input, dissipation and interaction between waves of different scales and directions and describes the slow evolution of wind wave energy spectra in time and space. There has been accumulated a good understanding of spectra evolution obtained from modelling and observations. The weakest link is in translating the acquired knowledge of energy spectra into predicting probability distributions of wave heights. The major shortcomings of the prevailing approach are: (i) it relies on the very restrictive assumption of narrow spectra, while most of the observed spectra are broad from the viewpoint of nonlinear interactions, (ii) it does not properly take into account wave nonlinear interactions, (iii) it assumes stationarity of the process. Very recently PI and RCoI found a way to evaluate numerically the higher moments of probability distribution (skewness and kurtosis) within the established framework of wave turbulence without these restrictions. Since the procedure is numerically expensive, we propose to parametrize all combinations of wave spectra and thus to obtain simple parametrizations of probability distributions. This will allow us to deduce from first principles a parametrization of probability distributions easy-to-use in operational forecasting for all the variety of sea states.The sea states predicted by the existing models or obtained as a result of direct measurements describe somehow averaged ("normal") sea states. There also exist short-lived transient states caused by sharp changes of wind, which are filtered out by such averaging. We argue that these ephemeral sea states might be responsible for disproportionate share of anomalously high waves. Such transient sea states have never been studied in this context. The time resolution of wind forecasts was far too low, there were no conceptual and numerical tools. Crucially for this project the situation has improved radically: the time resolution of wind forecasts is improving dramatically, while the PI and RCoI derived a generalized kinetic equation able to describe the fast evolution of the spectra, developed and tested the numerical code able to tackle this equation. Combining this with the authors' specially designed direct numerical simulation algorithm, we propose a clear path for examining probability distributions of wave heights of transient events linked to rapid changes of atmospheric forcing.On this basis this project aims to revolutionise modelling of random wind waves and freak wave forecasting.