EXTENDED REFRACTION DIFFRACTION EQUATION FOR SURFACE-WAVES

A modification of refraction-diffraction equation is developed for waves propagated over a bed consisting of substantial variations in water depth. The Galerkin-Eigenfunction Method is used to determine all terms in the wave equation. The resulting equation includes higher order terms of the bottom slope and the term proportional to the bottom curvature, as well as the evanescent modes. The theory is verified against other theoretical and experimental results related to waves propagating over a patch of sinusoidal ripples. Numerical examples demonstrate the practical applicability of the extended refraction-diffraction equation for undulating bottom of steeper slope.