Conclusion and Future Study

This chapter summarized generally accepted mechanisms that cause freak waves and we have described linear and nonlinear mechanisms in more detail. Four-wave

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quasi-resonant interactions have been shown to play an important role in deter-mining the statistical properties of surface elevation. This discovery, which is fairly new, is of some relevance to extreme wave forecasting. Previously, deviations from Gaussian behavior have been attributed only to bound modes. However, even in the most severe sea states, the kurtosis obtained from second-order theory rarely reaches values above 3.15. Moreover, contributions to wave height distribution from second-order theory are practically negligible (in the narrow-band approximation that are exactly zero). If waves are long-crested and sufficiently steep, the dynamics of the free waves can cause very strong departures from Gaussian behavior. Large values of the kurtosis can substantially change the tails of the probability density function for wave height and can increase the occurrence of freak waves.

Although nonlinear effects have been found to be important, some issues remain unresolved. First, we need an evaluation of the accuracy with which the kurtosis is estimated from spectra. BFI originally describes the asymptotic behavior, given an initial value, but in reality, there is no initial condition in the ocean. This should be verified in the near future. Second, we need to account for wave directionality.

In real sea states, directional effects are important. Directional contributions to the evolution of the kurtosis, using a modified nonlinear Schr¨odinger equation, have been described,⁴⁹and the effects of four-wave interactions only appear close to long-crested waves conditions.⁵⁰ A quantitative discussion of directional effects should be presented in the near future.

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Chapter 7