Linear Refraction-Diffraction Model for Steep Bathymetry

This paper describes the mathematical formulation, the numerical solution, and the validation of a linear refraction-diffraction model for steep bathymetry. The model involves two coupled governing equations derived from, respectively, the exact seabed boundary condition and the Laplace equation. It reduces to the extended and the original mild-slope model, when the seabed slope is small. Although the present approach is based on depth-integration of flow characteristics, it correctly accounts for the vertical component of the seabed fluid velocity. The formulation is based on the weighted-residual method, and the hybrid element solution is derived from a Galerkin approach. The capability of the present model to simulate flow velocity and wave amplitude over three-dimensional bedforms is examined in a parametric study. The computed results are compared with the original and extended mild-slope solutions and verified with those of a three-dimensional wave model. The present depth-integrated model has the same data requirements as other two-dimensional models, but provides accurate three-dimensional results with only a fraction of the CPU time that would be required by a three-dimensional model.