Abstract
The first- and second-order problems of wave transmission over a step in an oblique sea are solved using a Green's theorem integral equation with a finite-depth Green's function. The first-order transmission and reflection coefficients are shown to be consistent with previous results obtained by using the method of matching eigenfunction expansions (Newman), the variational formulation (Miles), and Galerkin method (Massel). Comparison of the second-order free wave agrees with Massel. It is shown that the ratio of the second- to first-order maximum amplitude can be over 0.2 for the range where the Stokes theory is valid and that at low frequency the second-order potential is more pronounced than the quadratic interaction of the first-order potentials.
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