Numerical simulations performed by nonlinear Schrodinger equation and high-order spectral method are compared with the laboratory experiments in this paper. A detailed assessment of the capability of the two wave models to descript irregular waves propagation is carried out. It is found that the HOS method shows a better agreement with the experiments in terms of simulating the wave parameters, while HOS method shows a little overestimation in predicting extreme waves.


Extreme waves, which occurs far more frequently than we have imagined, cause severe damages to offshore structures and vessels in recent years. It is critical to precisely predict the distribution of wave heights for the designing of offshore platforms. Besides accurate description of long term propagation of nonlinear waves in intermediate and deep water depth is also a key issue in ocean engineering. Usually, numerical models were used to implement this target.

One simple but powerful approach for the study of nonlinear slow modulated waves is the nonlinear Schrödinger equation which was first put forward by Zakharov (1968) adopting a spectral method. Hasimoto and Ono (1972) also derived the equation employing a multiple scale technique. The nonlinear Schrödinger equation is capable of describing slowly modulated waves which implies constraints in bandwidth and steepness. The NLS equation successfully predicts the phenomena such as envelope solitons (Zakharov and Shabat, 1972) and recurrence (Yuen and Ferguson, 1978). Onorato et al. (2001) studied the dynamics of freak waves using this equation. While this equation also has shortcomings that require the assumption of narrow-bandwidth and slow modulation. Dysthe (1979) later extended the NLS to fourth order and the resulting equation is the so called modified Schrodinger equation (MNLS). Trulsen and Dysthe (1996) went a step further by relaxing the constraint on the bandwidth. Many studies try to explain the formation of extreme waves adopting this method and this modified method is capable of describing phenomenon that is overlooked by NLS equation. For instance, Lo and Mei (1985) found the unequally growth of sideband perturbations and downshift of carrier wave using fourth-order nonlinear Schrödinger equation in a numerical study. Other features such as the split of wave packet is not observed in NLS equation either. Subsequent studies (Melville, 1982; Su, 1982) also confirmed the phenomenon. Zhang (2016) compared the MNLS model with the experiments in terms of wave parameters and exceedance distribution. Cousins and Sapsis (2016) found a way to forecast extreme waves employing the MNLS, and the results show high accuracy in random waves.

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