In this paper, we focus on the implementation and verification of an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions The time-domain numerical model is based on the fully nonlinear Boussinesq equations As described in Part I of this two-part paper, the energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves Wave runup on the beach is simulated using a permeable-seabed technique We apply the model to simulate two laboratory experiments in large wave basins They are wave transformation and breaking over a submerged circular shoal and solitary wave runup on a conical island Satisfactory agreement is found between the numerical results and the laboratory measurements

Boussinesq modeling of wave transformation, breaking, and runup. ii: 2d

SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters

The extended Boussinesq equations derived by Nwogu (1993) significantly improve the linear dispersive properties of long-wave models in intermediate water depths, making it suitable to simulate wave propagation from relatively deep to shallow water. In this study, a numerical code based on Nwogu's equations is developed. The model uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms retained by the model. The basic numerical scheme and associated boundary conditions are described. The model is applied to several examples of wave propagation in variable depth, and computed solutions are compared with experimental data. These initial results indicate that the model is capable of simulating wave transformation from relatively deep water to shallow water, giving accurate predictions of the height and shape of shoaled waves in both regular and irregular wave experiments.

Time-Dependent Numerical Code for Extended Boussinesq Equations

A parabolic model for calculating the combined refraction/diffraction of monochromatic linear waves is developed, including a term which allows for the dissipation of wave energy. The coefficient of the dissipation term is related to a number of dissipative models. Wave calculations are performed for a localized area of dissipation, based on a friction model for a spatial distribution of rigid vertical cylinders. The region of localized dissipation creates a shadow region of low wave energy, which may have important implications for the response of neighboring shore lines.

A.C. Radder

Papers

Verification of numerical wave propagation models for simple harmonic linear water waves