Extreme Events in Nonlinear Random Seas

[+] Author and Article Information
Francesco Fedele1

Department of Mechanical Engineering, University of Vermont, Burlington, VT 05405


Current address: Global Modeling and Assimilation Office, Code 610.5, NASA Goddard Space Flight Center, Building 32, Room S043-H, Greenbelt MD 20771; e-mail: fedele@gmao.gsfc.nasa.gov

J. Offshore Mech. Arct. Eng 128(1), 11-16 (Aug 30, 2005) (6 pages) doi:10.1115/1.2151202 History: Received March 25, 2005; Revised August 30, 2005

In this paper, the occurrence of extreme events due to the four-wave resonance interaction in weakly nonlinear water waves is investigated. The starting point is the Zakharov equation, which governs the dynamics of the spectral components of the surface displacement. It is proven that the optimal spectral components giving an extreme crest are solutions of a well-defined constrained optimization problem. A new analytical expression for the probability of exceedance of the wave crest is then proposed for the prediction of freak wave events.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The parameter λmax as function of the Benjamin-Feir index BFI for different values of the wave steepness εd

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Figure 2

Comparison between the analytical probability of exceedance of the wave crest Eq. 24 (solid line) and the empirical distribution computed from Monte Carlo simulations (dotted line). Here, BFI=1.15 and εd=0.05.

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Figure 3

The Benjamin-Feir index BFI as a function of the parameter γ of the JONSWAP spectrum

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Figure 4

Spectrum at the initial stage and when the highest crest is formed (BFI=1.15 and εd=0.05)

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Figure 5

Probabilities of exceedance




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