Numerical analysis of extreme waves in the North-Western Mediterranean area

Extreme sea waves have a great impact on the safety of navigation and coastal areas, however their prediction in operational forecasts is difficult and is generally based on spectral indices. Numerical simulations of the free surface Euler equations can be of notable help in the understanding of the statistical properties of a given sea state, and therefore to establish also the probability of extreme or rare events. In this study we performed phase-resolved simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We analyzed a number of sea-states occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. Namely, we produced statistics of the wave field, calculating crest distributions and the probability of extreme events from the analysis of long time-series of the surface elevation. The results show a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, while the Rayleigh distribution gives a significant underestimate. 

We looked for several kind of correlations between spectral quantities like angular spreading and wave steepness and the probability of occurrence of extreme events, finding an enhanced probability for high mean steepness seas and narrow spectra. It is also evident how the case study of the reported accident was not amongst the most dangerous sea states. Relating the skewness and kurtosis of the surface elevation to the wave steepness helped us to understand the discrepancy between theoretical and numerical distributions.