Abstract
Based upon the nonlinear model of Longuet-Higgins the joint distribution of wave surface slopes is theoretically investigated. It is shown that in the fourth order approximation, the distribution is given by truncated Gram-Charlier series. The types of wave-wave coupling interactions are related to the order of approximation to nonlinearity of sea surface, which eventually defines the truncated term of the Gram-Charlier series. For each order approximation, the coefficients in the series are modified comparatively to the corresponding ones for the previous order approximation. If the nonlinear effect of the kurtosis is considered, the wave surface must be as accurate at least as to the third order approximation, and with regard to skewness, the wave surface must be as accurate at least as to the fourth order approximation.
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