| Abstract: | A statistical analysis of unidirectional non-linear random waves is presented which is based on second-order random wave theory. The analysis technique is similar to a method which is available for the statistical analysis of a two-term Volterra series. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and eigenvectors of two real symmetric matrices, from which the cumulants, the characteristic function, and the probability density function of the surface elevation can be found. Various numerical examples are considered, and the possibility of extending the technique to deal with spreading seas is discussed. |
