Study On Statistical Characteristics Of Freak Waves In Multi-directional Random Wave Trains

Freak wave is a kind of catastrophic wave with great height and sudden strength,which poses a great threat to the safety of offshore structures and ships.At present,scholars have done a lot of studies on the occurrence probability,statistical characteristics and generation mechanism of freak waves and so on,but mostly concentrated in the two dimensional problems,while the actual wave is multi-directional irregular wave.Therefore,the research results on the occurrence probability,statistical characteristics and generation and evolution of freak waves in multi-directional random wave train can provide a basis for the safety evaluation and structural design of offshore buildings.Based on the measured data analysis and numerical simulation,the occurrence probability of freak waves in multi-directional random wave train and its relationship with the statistical characteristics of wave train are studied in this paper.In order to clarify the occurrence probability of freak waves in the actual ocean and its influencing factors,and discuss the formation of freak waves.Firstly,the relationship between the occurrence of freak waves and the statistical characteristics of wave train and the possible causes are studied by analyzing the measured wave data in many places.The results show that when the kurtosis of wave train is large,the Rayleigh distribution underestimates the occurrence probability of large wave height,and the Mer and GC distributions can give better predictions.The occurrence probability of freak waves increases linearly with the increase of kurtosis value.MER model can better describe the relationship between the occurrence probability of freak waves and kurtosis value.In addition,based on the wavelet spectrum and wave surface process of typical freak waves in the measured data,the generation types of freak waves are analyzed,and it is considered that the freak waves at sea may be caused by modulation instability and wave energy superposition.Secondly,based on the high-order spectral method,a long-term numerical simulation of multi-directional random waves with different directional distribution is conducted to analyze the influence of directional distribution on the statistical characteristics and occurrence probability of freak waves,and explore the generation and evolution of freak waves in unidirectional irregular wave train and multi-directional irregular wave train.The research results show that with the decrease of the directional distribution widthσθ,namely the narrower the width direction distribution,wave train is unstable,the maximum kurtosis value increase,a maximum of freak wave generation probability also increases gradually,σθ=10°is the direction distribution affect the critical value,when the width direction distribution standard deviation is greater than the value,direction will have little impact on the probability of freak wave occurrence.Whenσθ<10°,the correlation between the occurrence probability of freak waves and kurtosis becomes stronger with the decrease of the standard deviation of the direction distribution width,especially when s=800 and unidirectional waves,the occurrence probability of freak waves tends to be closer to the Mer prediction.With the increase of the direction concentration parameter s,the wave height and creast distribution gradually deviate from the Rayleigh distribution,and the wave height distribution is closer to the Mer and GC distribution.The relationship between kurtosis and the steepness of wave group is not affected by the direction distribution and the steepness of wave group is established:Kurtosis=11.66GF_w/GL_w.Finally by using the wavelet energy spectrum diagram,wave process line and wave train space evolution figure the formation process of freak wave is analyzed,the results show that the direction distribution width is very narrow(s=800 and∞),the freak wave generated under the action of a nonlinear modulation instability,and for a wave train with a wider directional distribution(s=0),freak wave is formed by wave space gathering of different directions.