UNDERSTANDING EXTREME WAVES VIA A VARIATIONAL WAVE ACQUISITION STEREO SYSTEM

We present a novel variational Wave Acquisition Stereo System (WASS) that exploits new stereo reconstruction techniques for accurate estimates of the spatio-temporal dynamics of extreme oceanic waves. We shall present a statistical analysis that explains the role of nonlinearities in the formation of large waves. When nonlinearities are negligible, ocean waves are usually modeled by the linear superimposition of a large number of elementary waves having amplitudes related to a given spectrum and random phases. In this case, large waves are due to the linear focussing of a wave group (Lindgren 1972, Boccotti 2000) and their crests and troughs are both Rayleigh distributed. If second-order nonlinearities are dominant, then the sea surface displays sharper narrower crests and shallower more rounded troughs. As a result, the skewness of surface elevations is positive, and wave crests are distributed according to the Tayfun model (Tayfun 1980). If, however, elementary waves also exchange energy nonlinearly via third order four-wave resonances, narrowband wave trains can undergo intense modulational instability enhancing the occurrence of large waves (Janssen 2003, Fedele 2008) and the distribution of crest heights deviates from the Tayfun model. This is confirmed by the wave-flume experiments in (Onorato et al. 2006) and the numerical simulations of the Dysthe equation (Socquet-Juglard et al. 2005), a special case of the Zakharov equation (Zakharov 1999). However, in broadband waves the Tayfun distribution appears to explain crest statistics well (Fedele 2008, Tayfun & Fedele 2007). The unusually wave crests observed in both the latter experiments and simulations are well explained by a recent Gram-Charlie