Marine accidents represent a great disaster from a socio-economical point of view. Although many cases can be related to human errors, accidents still occur due to the ferocity of the sea. Therefore, it would be of great benefit if warnings could be given as part of the standard marine weather forecasts. Within the framework of the E.U. project MaxWave and in order to contribute to the development of warning criteria, ship accidents reported as being due to bad weather conditions were analyzed. This investigation revealed that sea states characterized by two wave systems with different direction of propagation, also known as crossing or bimodal seas, often occurred at the presumed time of the accidents.
According to theoretical studies, crossing sea conditions may lead to the instability of wave packages, and hence increase the probability for the formation of extreme wave events. By using numerical simulations, this dissertation mainly discusses the statistical properties of the surface elevation in crossing sea states. In order to have enough samples to stabilize the statistical properties, many random realizations of the surface elevation have been reconstructed from a given input spectrum (i.e. the distribution of the wave energy). Since nonlinear interactions are mainly responsible for the formation of extreme wave events, nonlinear wave theories have been used to model the wave elevation: second--order wave theory is applied in deep and intermediate water depths; the Kadomtsev--Petviashvili equation is used for shallow water depths.
Sets of numerical simulations were performed by considering different angles between the intersecting wave systems, different degrees of nonlinearity, and different random phases. These experiments indicate that there are combinations of non--collinear wave trains that can produce higher amplitude peaks than in the case of sea states characterized by one wave system (i.e. unimodal sea). The formation of these large amplitudes, furthermore, contributes to modify significantly the statistical distribution of the surface elevation. The investigation of crossing sea states has also revealed that there are conditions at which an anomalous elevation (set--up) of the mean sea level takes place instead of an expected depression (set--down) of the free surface. In deep and intermediate water conditions, this set--up arises because of the nonlinear interactions between wave components with very different direction of propagation. In principle, this set--up has a positive contribution on the crest amplitude; the statistical analysis of many random time series, however, did not reveal any significant deformation of the probability density function.
