Numerical Investigation on Nonlinear Evolution Behavior and Water Particle Velocity of Wave Crests for Narrow-Band Wave Field with Gaussian Spectrum

The nonlinear evolution of initial narrow-band Gaussian spectrum wave field, as well as the water particle velocity of wave crests for Freak waves are investigated by phase-resolved numerical model of high-order spectral (HOS) method. The long-time evolution behavior (up to 2000 wave periods) are considered under the effects of initialized parameters, including initial spectral width, wave steepness and BFI. The effects of initial BFI on occurrence probability of Freak waves indicate various distinctive stages. Moreover, the evolution characteristics of spectral width, local wave steepness, BFI and kurtosis are analyzed. And near-periodic oscillating pattern of spectral width after its long-time evolution is obtained and effected by initial spectral width and wave steepness with different features. Besides, the positive (or negative) linear correlations between wave height extreme value and local wave steepness & kurtosis (or BFI evolution value) are effected by initial spectral width primarily. At last, the behavior of water particle velocity (including the extreme value) of Freak wave crest is discussed. And the nonlinear correlation between wave crest height and water particle velocity of wave crest is obtained quantitatively.