A Numerical Study On Freak Waves In2-dimensional Random Sea State

The Freak Wave in the ocean is a catastrophic event that appears from nowhere without alarm and disappears without a trace. Freak waves have been subjected to much attention in recent years due to their potentially severe damages to the vessels and offshore structures. In design practice, people concern more about forecasting the probability of freak waves occurrence, while most previous studies on freak waves focused on the mechanism of freak waves.In this paper, the generation of freak waves in a2-dimensional random sea state characterized by the JONSWAP spectrum are simulated employing a nonlinear fourth-order Schrodinger equation. Nine cases of experiments with different initial conditions are performed in our research in order to investigate the effect of initial wave parameters on the occurrence probability of freak waves. Firstly, the evolution of the unstable wave packet in deep water is analyzed. During the generation of freak waves, a single wave absorbs energy from neighbor waves, increasing its amplitude, reaching a maximum and then returns its energy back to other waves. This evolution can be viewed as a focusing-defocusing process.Secondly, the evolution of kurtosis, significant wave height, skewness and wave spectrum are analyzed as well. The results show that Benjamin-Feir index (BFI) is an important parameter to identify the presence of instability. The kurtosis presents a similar spatial evolution trend with the occurrence probability of freak waves and kurtosis is a good indicator for the freak wave amount. Freak waves in a random sea state are more likely to occur for narrow spectrum and small values of significant wave height. Skewness and significant wave height basically keep constant during the propagation. Skewness is dependent on initial wave steepness. The nonlinear interaction between waves leads to the transtfer of wave energy from the peak of wave spectrum towards higher and lower frequency, so the width of wave spectrum broadens and height decreases. Based on the previous discussion, the intrinsic relationship between freak waves in deep water and Benjamin-Feir instability is investigated. The formation of freak waves is mainly attributed to the quasi-resonant four wave interactions, which also causes Benjamine-Feir instability, rather than due to phase locked modes.At last, the wave height distributions are discussed. For the case that BFI<1.0, the simulation agrees well with the Rayleigh distribution; for the case that BFI>1.0, the wave height is also Rayleigh distributed in the initial stage because the modulation instability is not very strong. In other locations, Rayleigh distribution underestimates the probability of freak wave occurrence by more than one order of magnitude, and the deviation is more pronounced for large values of enhancement coefficient and small values of significant weight height. Wave crest distribution can’t fit Forristall distribution and Rayleigh distribution as well. As the evolution of waves approaches to the fully developed condition, MER distribution can describe the wave height well.