Run-up of dispersive and breaking waves on beaches

Transformation of waves on sandy beaches, their breaking, set-up and run-up are the main factors contributing to fluctuations in the water table and groundwater flow. In this paper, the run-up mechanisms have been studied using analytical models. In contrast to the standard models, the waves approaching the shoreline are assumed to be dispersive and the equivalence of the non-linear and linear solutions for the extreme characteristics of wave run-up, such as the height of maximum run-up and the velocity of run-up, are used. A linear system of equations for the run-up of breaking waves is developed. This system is based on the application of the mild-slope equation in the deeper area, where waves are dispersive, while the linear equations of shallow water are applied close to the shoreline, where the water depth is a linear function of distance. The dissipation factor in the shallow water equation has been formulated using its resemblance to the mild-slope equation for a non-permeable sea bottom. Application of the method is illustrated for various bottom profiles and wave characteristics, and theoretical results compared well with experimental data. These solutions of the run-up phenomena will assist future studies on wave-induced beach groundwater flow