Numerical Investigation On The Nonlinear Wave Evolution And Freak Wave Based On A High-order Spectral Method

Since the 21-st century,human activities at sea have become more and more frequent,and the development and utilization of marine resources has entered a new stage,while the prevention and control of marine disasters is facing new challenges.The freak wave is a kind of disastrous wave with high wave height,and the wave nonlinearity is one of the main reasons.This thesis focuses on the nonlinear wave evolution and freak wave characteristics,which provides a theoretical basis for establishing an effective warning system of marine disaster,and provides a calculation basis for the safety analysis of ships and offshore platforms.Numerical simulations based on the Higher-Order Spectral(HOS)method,combining both the Zakharov equation and the Nonlinear Schr?dinger equations,the influence of the third-order nonlinearity on the wave evolution and the characteristics of the freak wave is comprehensively analyzed,ranging from simple resonant and modulated wave trains,to unimodal and bimodal spectral irregular waves.A theoretical model of four-wave resonance in finite water depth was established based on the Zakharov equation.Combined with HOS numerical simulation,the influence of water depth on the four-wave resonance was revealed,and the critical water depth of the four-wave resonance was discussed.The study found that as the water depth decreases,the growth rate of daughter wave decreases,and the exact and near four-wave resonances are suppressed.When 6)? ≤ 0.57(6)is the wavenumber,? is the water depth),the four-wave resonance with crossing angle = 25?disappears,and when6)? ≤ 0.40,the four-wave resonance of all angles disappears.Using the three-dimensional fast Fourier transform,the influence of the bound wave on the daughter wave evolution is discussed,and the difference between the HOS simulation and the theoretical results of the Zakharov equation is successfully revealed.The influence of the wave steepness,spectral width and water depth on the modulation instability is carefully investigated.A transition phenomenon in the modulation instability is found.The duration of this transition is related to the growth rate of the modulation instability,The greater the growth rate,the shorter the transition time.When the growth rate is large enough,the transition phenomenon disappears completely.Besides,A phase-locked phenomenon in modulation instability was discovered.A series of HOS simulations were carried out to study the evolution of unimodal spectral irregular waves and the freak waves.Evolution of the nonlinear wave statistics and features of the freak wave in different wave steepness,spectral width and water depth were investigated.Wave statistics including wave spectrum,exceedance probability of wave crest,probability of surface elevation,occurrence probability of freak wave,and freak wave shape were analysed.Based on the three-parameter Weibull distribution,a third-order semi-empirical distribution for the exceedance probability of wave crest was successfully established,which effectively improved the accuracy of the calculation of the wave crest distribution.It is verified that the Benjamin-Feir Index is related to the occurrence probability of freak wave,and a prediction model of the occurrence probability of freak wave is established.Further,a series of numerical simulations were carried out to analyze the wave evolution of the bimodal spectral irregular waves and the characteristics of freak waves.The influences of crossing angle,spectral width and directional spreading are illustrated.It is found that,in the long-crested crossing seas,when the propagation angle is between 40 degrees and 60 degrees,the interaction between the wave systems will lead to a significant enhancement of the third-order nonlinearity,and the generation probability of freak waves is greatly increased;in the short-crested crossing seas,the propagation angle has no obvious effect on the evolution of waves and the probability of freak waves.In order to describe the effect of modulation instability in bimodal spectral waves,a new Benjamin-Feir Index is proposed,and based on this,a prediction model for the occurrence probability of freak waves in bimodal spectral irregular waves is established.Compared with the traditional Benjamin-Feir Index,this new factor includes the effect of interactions between different wave systems,so it can more accurately measure the influence of third-order nonlinearity,and further improve the prediction of the probability of freak waves.