| In this paper, the sea surface elevation for nonlinear random waves is represented by using Hermite polynomial expansion,
(For the equations please see the PDF file.)
in which, (For the equations please see the PDF file.), is normal process; Hn (Z) is n-order Hermite polynomial. The coefficients Cn (n=1, 2, 3, ---) in this model can be obtained from the moments of sea surface elevation, μm (m=2, 3, ---) through following relationship:
(For the equations please see the PDF file.)
In the third order approximation, the coefficients Cn (n= 1, 2, 3) are analytically expressed as follows:
(For the equations please see the PDF file.)
In addition, the bispectrum of nonlinear random waves under the second order approximation is derived,
(For the equations please see the PDF file.)
The new model in this paper is another formula of Longuet-Higgins’ nonlinear model for random waves. |
