# Effect of a harmonic surface pressure on wave propagation over a beach

## TL;DR

This paper studies how harmonic surface pressure affects wave behavior on beaches using a mathematical technique.

## Contribution

A novel finite Fourier transform method is used to model wave propagation with surface pressure effects.

## Key findings

- Wave trapping can occur under specific surface pressure conditions.
- The method works for various beach shapes and bottom corrugations.
- Streamlines were visualized for different beach types.

## Abstract

The objective is to study the harmonic forced wave motion over a beach by a finite Fourier transform technique. The constructed approximate solution has a logarithmic singularity at the shoreline. It accounts for reflexion and local perturbations. Trapping of waves may take place for particular choices of the applied surface pressure excess. The case of a wave incident against a cliff with horizontal bottom is solved exactly. The method deals invariably with a variety of bottom shapes, including the case where there is an additional corrugation of the bottom on a finite interval. Other bottom boundary conditions than impermeability can be treated as well. The results may be of interest in several practical applications, in particular the evaluation of the reflected wave. Numerical applications for a plane sloping beach, a parabolic-type beach and a shelf-type beach are presented and the systems of streamlines have been drawn over and in the proximity of the beach.