Numerical Simulation Of Freak Waves In Deep Water

Freak wave is one of ocean disasters with great damage. The investigation on this phenomenon still lies in its early age as far, so its generation mechanism and probability is obscure. Now numerical simulaiton of freak wave in deep water are mainly based on linear superposition methods or cubic nonlinear Schroedinger equation at home and abroad, however the definition of freak wave indicates that higher-order nonlinearity interaction among wave components is very important for the generation of freak wave and needs to be considered, so an important motive of this paper is to establish a four-order nonlinear numerical wave model to simulate formation of freak waves, and further study its possible coherent mechanism while some involved factors is discussed intensively.In this paper a nonlinear numerical wave model in deep water based on modified forth-order nonlinear Schroedinger equation in movable coordinates, which was derived with the potential of the induced mean flow effect considered, and this model can overcome some shortcomings of the models of cubic nonlinear Schroedinger equation or linear superpose methods. This nonlinear wave model is solved by a standard split-step, pseudo-spectral method. Numerical model is checked by the evolution of periodic wave group and soliton envelope.Sideband instability, namely Benjamin-Feir instability, exists in the evolution of slowly modulated periodic wave train, and can cause a local exponential growth in the amplitude with time. This characteristic can be performed perfectly by the established model of this paper, so the model is used to simulate formation of freak wave here. A series of numerical experiments for the evolution of wave train to form freak waves are carried out with the initial conditions of one pair or more pairs of sideband perturbation wave trains and random wave characterized by JONSWAP spectrum. In order to verify the applicability of the wave model for simulating wave train evolution and freak wave generation in deep water, some numerical results are compared with corresponding laboratory experiments. All the results have shown that the numerical model of this paper can better simulate the evolution of wave train and generation of freak wave under the initial conditions of sideband disturbance and random wave.At present, the study of freak wave simulation mainly focuses on wave profile, however its inherent energy mechanisms and influence factors are seldom discussed perfectly and systemically. So on the basis of freak wave occurrence, variation of spectrum is discussed to understand its possible mechanism. The important influence of high-order nonlinearity on freak wave generation is also studied through comparing the wave model of this paper and the model of linear equation and cubic Schroedinger equation. And some relavant factors such as scale factor, pairs of initial siandband disturbance and wave steepness for sideband disturbance initial condition, energy parameter and enhancement coefficient of JONSWAP spectrum and random initial phase for irregular wave initial condition are also analyzed to understand the relative influence on freak wave generation. The results have shown that three-order and four-order nonlinearity plays an important role in freak wave generation, and probability of freak wave generation increases with the growth of number of unstable sidebands, number of initial sideband disturbance, wave steepness, and energy parameter and enhancement coefficient of JONSWAP spectrum. In addition, distribution of initial random phase also has a great effect on freak wave generation.