Pseudospectral approach for scattering of water waves

Wave propagation models for scattering of water waves are developed based on the mild-slope equation. The pseudospectral Fourier approach is used to reduce the mild-slope equation to a set of ordinary differential equations for the modified potential, φ √CC_g, at collocation points in the alongshore direction. The wave field is then decoupled into a series of wave modes including all forward and backward propagating modes. Ignoring the backward wave field as a first approximation, a wide-angle parabolic model is derived. When the backward wave field is important, both forward and backward wave fields are obtained by constructing the Bremmer series solution. A small-angle parabolic model is also developed for comparison. Numerical results are presented for wave refraction over an equilibrium beach profile and wave focusing over a submerged circular shoal on a flat bottom. The importance of the backward scattering is illustrated by the latter example.