A NOTE ON APPLICATIONS OF THE MILD-SLOPE EQUATION FOR RANDOM WAVES

Based on the formal derivation of the mild-slope equation (Smith & Spr inks, 1975), the neglected 'forcing terms' are rederived. It is shown that the slope terms are of order epsilon(2), which are negligible acc ording to the mild-slope assumption, where epsilon = /del h//kh repres ents the classical definition of small parameter for mild-slope. It is found that the curvature terms depend not only on epsilon but also on the wave frequency and the terms have considerable effect on wave pha se in the lower range of wave frequencies. Therefore, in the broad wav e spectrum case, the curvature terms discarded by Smith & Sprinks (197 5) are necessary to accurately predict waves over a bottom with severe curvatures.