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

Abstract

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 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 botom. 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.

A Parabolic Equation for Wave Propagation over Porous Structures

“…10. It is observed from all the figures that the present model results are in much closer agreement with the experimental data than those of the linear model (Dalrymple et al, 1989) for an impermeable shoal. For any case that involves wave refraction, diffraction, and energy dissipation, it is evident that the present model is capable of accomplishing this job.…”

Generalized evolution equations for nonlinear surface gravity waves over two-dimensional topography

“…Our derivation is along the lines of Chu & Mei (1970), generalized to a multi-frequency and multi-directional wave field utilizing an angular spectrum decomposition of the wave field (e.g. Dalrymple et al 1989), and extended to higher order in the bound wave components to support the transition to shallow water. The effects of topographical features on the wave propagation are included through a scattering mechanism (e.g.…”

Experimental verification of horizontal two-dimensional modified mild-slope equation model

“…It has not only been used in its original form of elliptic equation but also provided the basic governing equation for the development of other wave propagation models such as parabolic model (Radder, 1979), hyperbolic model (Copeland, 1985) and angular spectrum model (Dalrymple et al, 1989).…”