Based on improved Longuet-Higgins wave model, four wave focusing models for freak wave generation (1.extreme wave model +random wave model; 2. extreme wave model +regular wave model; 3. phase interval modulation wave focusing model; 4. Number modulation wave focusing model with the same phase) are proposed. By using different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time. Numerical simulations are carried out in a 2-D wave focusing model, which is presented based on enhanced high order spectral (HOS) numerical method and validated by comparison of numerical results with experimental and theoretical ones (linear waves). The fully nonlinear model of formation of extreme wave is conducted based on the enhanced HOS numerical technique. By comparing the simulations with experimental study presented by Baldock (1996), validation of the numerical model is verified, and the importance of wave-wave nonlinear interactions is emphasized. Numerical results show that the divergence of surface elevation at the focus point from the linear input solution, the downstream shifting of focus time and the downstream shifting of the focus point result from the wave-wave nonlinear iterations. Improving Longuet-Higgins model, four focusing models of formation of small-scale freak waves are obtained. Investigations of parameter Hmax/Hs characterizing freak waves appearing to depend upon the energy distribution methods are then realized. Adjusting energy distribution in the four models, freak wave phenomenon is achieved with different Hmax/Hs in finite space and time. The present work is conducted without bathymetry, directional or current.


In recent years the freak phenomenon in the ocean has become a topic of intensive study. Such a wave may lead to damage of ships and offshore platforms and to deaths (Tsai et al, 2004, Haver and Andersen, 2000).

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