The theory of quasi-determinism, for the mechanics of linear random wave groups was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. In this paper the first formulation of Boccotti’s theory, particularized for long-crested waves, is extended to the second-order. The analytical expressions of the nonlinear free surface displacement and velocity potential are obtained. The space–time evolution of the nonlinear wave group, when a very large crest occurs at a fixed time and location, is then shown. Finally the second-order probability of exceedance of the crest amplitude is obtained and validated by Monte Carlo simulation.
Nonlinear Space–Time Evolution of Wave Groups With a High Crest
Contributed by the OOAE Division for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received November 6, 2003; final revision, October 6, 2004. Review conducted by: J. Niedzwecki.
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Arena, F., and Fedele, F. (March 23, 2005). "Nonlinear Space–Time Evolution of Wave Groups With a High Crest ." ASME. J. Offshore Mech. Arct. Eng. February 2005; 127(1): 46–51. https://doi.org/10.1115/1.1854705
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