The generation of edge waves by a wave-maker

A theory is developed to describe the generation of edge waves on a uniform beach by a wave-maker. The theory is based on the linear shallow-water equations. The wave-maker is a vertical plate spanning between the shoreline and the paddle axis offshore, and oscillates periodically in the alongshore direction. It is found theoretically that only propagating modes exist: the evanescent modes are always accompanied by incoming waves from offshore and are not permissible in this case. For each propagation mode the cross-shore variation is described by the Laguerre polynomial with an exponentially decaying amplitude. Laboratory experiments are performed and experimental data are compared with theoretical solutions. Since the viscous damping is ignored in the theory, the wave amplitudes for the experimental data are usually lower than the theoretical predictions. However, the cross-shore variations of the wave form are predicted well by the theory. Furthermore, from both theoretical and experimental data, it is shown that wave fields are dominated by the Stokes edge-wave mode in the low frequency range, F<0.5 Hz.