Investigations On Occurrence Probability Of Freak Waves Under Various Wave Conditions

With the increase of marine development activities,the situation that offshore structures and offshore vessels encounter harsh marine environment is becoming increasingly prominent.Freak waves with large wave height and strong nonlinearity pose a great threat to the safety of offshore structures,ships and personnel at sea.Therefore,it is of very important practical and guiding significance to comprehensively and systematically study the occurrence probability of freak waves under various wave conditions and the evolution characteristics of extreme waves.Firstly,by means of the fully nonlinear numerical model based on High Order Spectral(HOS)method established in this paper,unidirectional random wave trains with unimodal spectra are simulated for a long-time duration.The influence of BFI value and relative water depth kph on nonlinear statistical parameters is emphatically analyzed,and the contour of the maximum kurtosis affected by both BFI and 1/(kph)is given.The statistical results show that the modulation instability is still affected by the relative water depth kph under the so-called classical deep-water condition,that is,kph>?,and the statistical kurtosis value of the nonlinear numerical simulation results is generally larger than the theoretical prediction.At the same time,the relationship between the occurrence probability of freak waves and statistical parameters is studied,and the quantitative relationship between the occurrence probability of freak waves Pfreak and kurtosis value in random wave trains under various wave conditions is statistically obtained:Pfreak=0.29kurtosis-0.82.In addition,the evolution processes of typical freak waves in unidirectional random wave trains are analyzed,and two main types of generation process are found:nonlinear modulation instability dominant and wave group interaction dominant.Secondly,continuous long-time simulations are carried out for the unidirectional random wave trains with bimodal spectra,and the influence of Intermodal Distance(ID)and Sea Swell Energy Ratio(SSER)on the nonlinear statistical parameters of wave trains is analyzed.It can be found that,with fixed significant wave height Hs and mean zero-crossing period Tz,the occurrence probability of freak waves or extreme large waves in bimodal random wave trains is smaller than that of unimodal random wave trains,and the more uneven the distribution of bimodal spectrum energy and the smaller the frequency interval between two peaks,the greater the occurrence probability of freak waves or large waves.Meanwhile,the quantitative relationship between the maximum kurtosis of unidirectional bimodal waves and SSER,ID is established,and the quantitative relationship between the occurrence probability of freak waves Pfreak and kurtosis value of bimodal waves is consistent with that of unimodal waves.Besides,the comparison between the mixed wave field and the corresponding single independent systems demonstrates that the bimodal wave field is not simply equivalent to the linear superposition of corresponding unimodal wave field,and the wave energy being distributed among frequencies plays a major role.Then,based on the wave parameters of the unidirectional unimodal waves and the unidirectional bimodal waves,the continuous long-term numerical simulation of multidirectional unimodal random wave trains with various directional spreading parameters s and multi-directional bimodal random wave trains with various crossing angles ? are carried out.It is found that the larger the directional spreading parameters s is,the stronger the instability of the wave train is and the greater the probability of freak waves is.However,in the crossing wave field,the influence of crossing angle ? on the instability of wave trains is related to the values of SSER.The crossing angle has a greater influence on the waves in sea-swell energy equivalent wave condition(SSER=1.0),and the freak wave is more likely to occur when the crossing angle ?=40°than ?=0°.Crossing angle ? has no obvious effect on the wave field dominated by sea-swell(SSER<1.0)and by wind(SSER>1.0).Finally,the formation process of freak waves dominated by the interaction between wave groups,found in the numerical simulation of unidirectional random wave train,is simulated and analyzed.The physical experiment of double-wave-group focusing is conducted to reconstruct the formation process of this type of freak waves.The evolution characteristics of the interaction between two wave groups and the nonlinear interaction between wave groups in the process of forming freak waves are explored by combining with numerical analysis.It is found that the frequency spectrum and dispersion of the wave group with higher peak frequency change obviously in the process of double-wave-group focusing,which is caused by the thirdorder nonlinear interaction between these two wave groups.Based on the research results of this paper,according to the initial wave parameters of a given wave field,the occurrence probability of freak waves can be predicted by using the quantitative relationship between the occurrence probability of freak waves and the characteristic parameters of wave conditions.It can provide practical reference value for the prediction of extreme wave and extreme sea state,and provide important engineering guidance for the structural design and safety protection of offshore buildings and ships.