Nearshore wave modeling with high-order Boussinesq-type equations

The accuracy of using high-order Boussinesq-type models as compared to the typical order models is examined in this paper. The high-order model used is the two-layer model of Lynett and Liu in 2004, which captures both linear and nonlinear wave evolution up to kh approximate to 6. The physical situations examined all involve nearshore breaking, and an eddy-viscosity type breaking model is adopted for the two-layer model. One-horizontal dimension setups are the focus of this paper. It is shown that high-order models show significant benefit very near to the breaker line. For regular incident waves, the overshoaling seen in the one-layer ("fully nonlinear" extended Boussinesq) model is due to rapid increase of energy in the fifth and higher harmonics. These high-order nonlinear components are captured well in the two-layer model. The two-layer model also exhibits a noticeable accuracy increase for cnoidal waves breaking on a slope. For regular wave evolution over a bar, the high-order models are in good agreement with experiment, correctly modeling the free short waves behind the step. Under irregular wave conditions, it is likewise shown that high-order nonlinearity is important near the breaker line and the outer surf zone. Using SwashX field data, spectral comparisons are made and discussed.