Directional Effects on Freak Wave Prediction

Abstract

Based on the Monte Carlo simulation of the two-dimensional nonlinear Schr¨odinger equation, the dependence of kurtosis on the directionality is verified. The parametric survey has been carried out to obtain the general behavior of kurtosis as functions of Benjamin-Feir index and directional spectrum bandwidth in two dimensional wave number space. As directional dispersion effect becomes significant, the kurtosis is monotonically decreased in comparison with the unidirectional case. On the basis of the Monte Carlo simulation, the new formula of kurtosis including the directional spectrum bandwidth is proposed. The proposed formula can predict the kurtosis from directional spectra within 10% error.