ON THE TRANSMISSION OF WATER-WAVES OVER A SHELF

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 an d reflection coefficients are shown to be consistent with previous res ults obtained by using the method of matching eigenfunction expansions (Newman), the variational formulation (Miles), and Galerkin method (M assel). Comparison of the second-order free wave agrees with Massel. I t is shown that the ratio of the second-to first-order maximum amplitu de 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 th an the quadratic interaction of the first-order potentials. (C) 1997 P ublished by Elsevier Science Ltd.