| Extreme waves pose a great threat to ocean structures and marine vessels.With the change of global climate,the occurrence of extreme waves is increased in both offshore and coastal areas,hence the reaserch of extreme waves is of great pratical significance.Extreme waves are highly nonlinear and random,hence,very difficult to capture accurately in laborotroy and/or in numerical simulations in relatively short time duration.However,the accurate prediction of its occurrence and the imporved understanding of the underlying occurring mechanics are very important.In this study,the formation mechanisms(including energy focusing and modulation instability)of extreme wave which are more commonly used are adopted,and the short-time wave group is taken as the research object,the generation and nonlinear evolution of extreme waves are further investigated by means of scaling model experiment and numerical simulation,and their nonlinear characteristics are described in detail.The main finds/novelties are summarized as follows:A set of experiments is designed to investigate the evolution of the extreme events formed in single Gaussian wave group and dispersive focusing wave group in finite water depth.The methodology of Hilbert-Huang Tranform(HHT)is used to analyze the instantaneous frequencies of the intrinsic mode functions that constitute a wave group.It is found that the wave breaking occurs when flmax/f0(can be viewed as frequency modulation ratio)? 2 in which fimax is the first-order instantaneous frequency when the maximum crest occurs and f0 is the carrier frequency.The wave energy across the spectrum is focused quickly before the breaking,and the instantaneous frequency increases suddenly.The breaking occurs when the frequency modulation ratio reaches 2.The instantaneous frequency decreases afterwards.The evolution of Hilbert spectrum of a wave group is investigated as well based on the experiment of the evolution of extreme waves in single Gaussian wave group and dispersive focusing wave group.The characteristics of energy dissipation in time domain are identified and it is found that the energy dissipation mainly occurs between the maximum crest and the adjacent front trough of the wave group in finite water depth.Before the wave breaking,as it is approaching the focusing point the energy of the wave group is mainly concentrated near the maximum wave crests which may across 2?3 wave periods;Meanwhile,the energy at higher frequencies increases gradually.After the wave breaking,the energy at higher frequencies decreases,and the maximum dissipation area is found to be localized at the area between the peak and the previous trough.The corresponding numerical simulations are carried out using high-order spectral(HOS)numerical wave model.The model is validated by comparing with the experimental results,and is extended to explore the parameter space that is not investigated in the experiments.It is found that there is an exponential relationship between the maximum crest and the wave steepness when extreme wave is formed during the evolution:?max=A1exp(-SG/t1)+y0.SG is the global wave steepness,?max is the maximum crest/the maximum wave surface elevation,and A1,t1 and y0 are the fitting parameters.The exponential growth velocity A1 is found to be the function of the wave group structure.With the decrease of the bandwidth of the wave group,A1 increases and the maximum wave surface elevation grows more quickly with wave steepness.In conclusion,the nonlinear characteristics of extreme waves in a single wave group are investigated using physical experiment and numerical simulations.The extreme wave is characterized by a large group of variables,including the instantaneous frequency,the energy dissipation,amplitude spectrum,Combined Degree of Nonlinearity...The effect of the initial wave group on these parameters is investigated.A new wave breaking index is proposed,and can provide a valuable reference for better describing the intrinsic mechanism of extreme waves. |
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