Numerical Study on the Non-linear Behaviour of Steep Isolated Unidirectional Waves

This paper presents some results of a study on the non-linear features of steep isolated 2D waves conducted at the Dept. of Naval Architecture, Ocean and Environmental Engineering of the University of Trieste in the frame of a wider research project financed by CETENA SpA on the wave loads on ships and marine structures in severe sea conditions. The analysis is here conducted by numerical simulations, thus solving the fully non-linear flow field by means of a BEM technique, and specifically it regards the non-linear effects deriving from the wave-wave interaction due to the frequency focusing of the component waves in a given spectrum [Codiglia, 2002; Contento et al., 2001]. It is shown that the shape of the wave spectrum computed at different stations in the direction of propagation is modified as a consequence of the nonlinear interaction of the component waves. In particular new high frequencies appear at positions close to the focusing station with non-negligible amplitudes. Moreover the highest wave is magnified by several unit percent (up to 15%) compared to simple linear predictions and the phase speed of the new high frequency components doesn’t fulfil the dispersion relation but it is locked to the phase speed of the highest component in the discrete input spectrum. Each numerical result here shown is supported by analogous experimental data presented by Chaplin [1996] and Chaplin et al. [1997]