Distributions Of Nonlinear Wave Base On High-Order Spectral Numerical Model

Extreme waves are a wave with a low probability of occurrence,a sudden occurrence,a high wave height and a strong destructive force.There are many theories about the causes of extreme waves.There is a theory that in deep water because of the third-order nonlinear interaction of waves,the existence of modulation instability will increase the probability of extreme wave occurrence,and the corresponding wave height distribution will deviate from the linear theory of the Rayleigh distribution results.There are many theories of wave height distribution to describe the wave distribution under nonlinear action.It is very helpful for predicting the probability of extreme wave occurrence to determine the appropriate wave height distribution form which can describe the wave under nonlinear action.In this paper,a complete nonlinear numerical wave pool based on the High-order spectral method is added to the non periodic wave-making boundary and the wave-extinction boundary as a numerical model.Under two-dimensional conditions,the propagation and evolution of multiple wave regimes with different significant wave heights,different spectral widths and different peak periods under deep water conditions were simulated using JONSWAP spectra.The wave height statistic parameters,frequency spectrum,skewness value,kurtosis value,extreme wave generation probability and the change of wave propagation in different wave conditions are discussed.The results show that the spectrum of wave has the decrease of spectral peak,narrowing of spectral width,the skewness value is correlated with the wave steep value,the wave crest value is correlated with the generation probability of the extreme wave,and the peak value of the wave condition(>0.6)of the BFI index is increased obviously,and the BFI can be used as the basis for judging whether the wave condition will be adjusted unstable.The wave height distributions,Rayleigh distributions,Boccotti distributions,GC distributions,MER distributions and Generalized Boccotti distributions of 5 different theories are selected as theoretical wave models.The wave sequences at different propagation distances in different wave conditions are selected and compared with the theoretical distributions.In the initial stage of wave propagation,the wave height distribution will be smaller than the Rayleigh distribution,and the generalized Boccotti distribution in the Wave column with a smaller kurtosis value(<3.3)conforms well.For the wave condition of the medium kurtosis(3.3-3.6),the extreme wave height is coincident with the results of MER and GC distributions,wave height is less than 1.8 times the significant wave height,which is more consistent with the generalized Boccotti distribution.The maximum value of extreme waves is far beyond the predicted results of several wave distributions for the larger kurtosis.In the wave crest and trough distribution,the Rayleigh distribution,the second-order nonlinear wave crest and the trough distribution and the thirdorder nonlinear wave crest and the trough distribution of the third Order nonlinear correction are compared.In a wave condition with a peak value of less than 3.5,the third-order distribution is in good agreement with the measured results,and the large peak and valley values deviate from the third-order distribution in the larger peak-value wave condition.