Estimation of Joint Probability Density Functions of Surface Elevation and Slopes for a Nonlinear Random Sea

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Laboratory experiments were conducted to measure the joint distribution of the surface elevation and slopes for nonlinear random waves. A method for estimating the joint distribution of surface elevation and slopes was developed by applying the principle of maximum entropy. The estimated distributions were compared with the measured distributions, the Gram-Charlier series and bivariate Gaussian distributions. The present method was found to produce a similar distribution to that observed.The relationship between skewness and kurtosis was theoretically and experimentally investigated. The effects of reflected waves on the joint distribution of the surface and slopes were also investigated. The theoretical conditional distributions ofbased on a simple nonlinear wave model reproduced the dependence on the representative wave slope and were in good agreement with the laboratory observations.