Models for very wide-angle water waves and wave diffraction. Part 2. Irregular bathymetry

A wide-angle model for water-wave propagation on an irregular bathymetry is developed based on the linear mild-slope equation. The spectral model decomposes the incident wave wavetrain into directional modes, or an angular spectrum. The effect of the bottom topography is shown to force the generation of additional directional wave modes. Nonlinearity is incorporated in the model by correcting the wave parameters iteratively using an empirical nonlinear dispersion relationship which is approximately valid over the entire range of water depths. Numerical examples are presented for waves incident on a transverse bar field, a laboratory experiment involving wave focusing over an elliptic shoal on a sloping beach for which detailed measurements are available and for waves focusing behind a circular shoal resting on a flat bottom. The application of the model is limited to cases in which the model domain is rectangular and the depth variation in the lateral direction is small if waves of large incident angle are modelled.