Abstract
A method to estimate the statistical properties of non-linear short-crested irregular waves without any limitation regarding the directional spreading or the spectral band width is presented which is based on the secondary interaction theory of surface waves. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and the eigenvectors of two real symmetric matrices and the probability density functions of surface elevation can be obtained using the so-called Saddle Points Method. Numerical investigations regarding the effect of shortcrestedness on the statistics of wave amplitudes are performed. And the method is also used to analyze full-scale data measured in stormy sea states and is shown to be a powerful tool for the estimation of the statistical properties of the directional sea.
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