Wave-induced set-up and flow over shoals and coral reefs. Part 1. A simplified bottom geometry case

An analytical approach was used to model the wave-induced set-up and flow through simple shoal geometry when water depth is a linear function of the distance. Two different approaches were applied to parameterize the energy dissipation due to wave breaking. The resulting set-up height and flow velocity were determined and their dependence on the geometry of the shoal and offshore forcing was demonstrated. The extension of the solution to a more complicated bathymetry and verification against the experimental data will be given in the second part of the paper.