On the Transformation of Directional Random Waves Under Combined Refraction and Diffraction

A method is presented for calculating the transformation of directional random waves under combined refraction and diffraction. The frequency spectrum, the cross-power spectrum, and the significant wave height of the refracted and diffracted waves are evaluated by introducing a spatial transfer function which satisfies the mild slope equation. A practical method for estimating the directional spectrum of random waves in the shadow region of a breakwater is presented. Numerical results for the directional spectrum along a coast with parallel depth contours are compared with theoretical results obtained by Longuet-Higgins. Finally, the distributions of significant wave height of random waves are presented for a jetty on a sloping beach and for a circular shoal on a horizontal bottom.