Effect of nonlinearity on statistical distribution of maxima Of Sea Wave surface

Based on the nonlinear model of random sea waves which is exact to the second-order, the joint distribution of wave surface elevation and its first-and second-order derivatives with respect to time is derived by using the development of characteristic function and calculation directly each order moment. From the above joint distribution the statistical distribution of the maxima of sea wave surface is derived. The derived distribution is physically determined by both sea wave frequency spectra which is in the sense of linearity and the second-order wave-wave interaction. When nonlinear effect is neglected, the derived distribution of maxima of sea wove surface is reduced to that derived by Cartwright and Longuet-Higgins.