Step Approximation on Water Wave Breaking and Dissipation over Variable Bottoms across the Surf Zone

This study investigates the combined effect of the breaking and energy dissipation of water waves by variable bottoms across the surf zone. The shoreline is set up as a partially reflecting vertical wall in the solution technique, with shelves between the steps that approximate the geometric profile of the varied bottom over the surf zone. The eigenfunctions over the shelves are matched on the connecting step using the conservations of mass and momentum. The impacts of breaking and energy dissipation are implemented in the proposed eigenfunction matching method using the energy-dissipation factors, which are modeled by empirical formulas. The proposed model is validated by comparing its results with the experimental data available in the literature. Some benchmark results of wave scattering by a rectangular breakwater near a partially reflecting vertical wall are provided and discussed. In addition, wave breaking and dissipation in the proposed model using different empirical formulas are discussed.