| A Boussinesq-type model has been developed to describe the wave transformation in the nearshore region. The model is fully non-linear up to O(μ 2) where μ is the wave length non-dimensionalized by the water depth. The model is derived from the fundamental equations of continuity and momentum by assuming that the motion in the surf zone is rotational. This leads to a formulation wherein the terms in the momentum equation that describe breaking appear as functions of the vorticity generated in the roller region of a breaking wave. Thus, in addition to the wave height evolution, the model is able to predict the velocity field due to the short wave motion in the surf zone. This feature is an improvement over the existing formulations for breaking waves using Boussinesq equations.; The equations are solved numerically using finite-difference methods. A fourth-order Adams-Bashforth-Moulton predictor-corrector method is used for time-stepping and a combination of second-order and fourth-order scheme is used for evaluating the spatial derivatives. An absorbing-generating boundary condition is used at the offshore boundary to specify the incoming waves and to absorb the reflected/outgoing waves. A shelf with finite but very small water depth is used at the shoreline. Breaking is initiated when the maximum of the slope at the front face of the waves exceeds a certain limit. The boundary conditions needed to solve for the vorticity are obtained from an analysis of weakly turbulent hydraulic jumps.; Comparisons to semi-analytical results are presented for the case of solitary wave propagation and shoaling. Very good agreement between the model results and experimental data is obtained for the wave heights, wave set-up, the velocity field and the undertow. The model performance with regard to the wave mass flux, the radiation stress, the wave speed, the development of vorticity in the surf zone and the development of the roller is also presented. |
