The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI = Hmas/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in bleaking waves and such occurrence in deep water is larger than that in shallow water.
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral （HOS） method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform （FFT） algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.
Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves （a. extreme wave model ＋ random wave model; b. extreme wave model ＋ regular wave model; e. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase） are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.
