On weak reflection of water waves

The weak reflection of monochromatic water waves is studied for the cases of slowly varying water depth. A coupled system of equations for the forward-scattering (transmitted) and the backward-scattering (reflected) wavefields are derived from the mild-slope equation (Smith & Sprinks 1975). Parabolic approximation is then used to simplify the equations for the diffraction factor. An iterative numerical scheme is proposed to compute the resulting equations. The scheme converges very quickly for the cases of weak reflection. The accuracy of the present approach is shown by comparing with numerical results obtained by a hybrid finite-element formulation.