On the Estimation of the Kurtosis in Directional Sea States for Freak Wave Forecasting

Based on Monte Carlo simulations of the nonlinear Schrodinger equation in two horizontal dimensions, the dependence of the kurtosis on the directional energy distribution of the initial conditions is examined. The parametric survey is carried out to obtain the behavior of the kurtosis as function of the Benjamin-Feir index and directional spread in directional sea states. As directional dispersion effect becomes significant, the kurtosis monotonically decreases in comparison with the unidirectional waves. A parameterization of the kurtosis estimated from directional spectra is proposed here; the error of the parameterization is at most 10%. The parameterization is verified against laboratory data, and good agreement is obtained.