Experimental investigation of the harmonic generation by waves over a submerged plate

Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater.     

Wave dissipation by vegetation with layer schematization in SWAN

The energy of waves propagating through vegetation is dissipated due to the work done by the waves on the vegetation. Dalrymple et al. (1984) estimated wave dissipation by integrating the force on a cylinder over its vertical extent. This was extended by Mendez and Losada (2004) to include varying depths and the effects of wave damping due to vegetation and wave breaking for narrow-banded random waves. This paper describes the wave dissipation over a vegetation field by the implementation of the Mendez and Losada formulation in a full spectrum model SWAN, with an extension to include a vertical layer schematization for the vegetation. The present model is validated with the original equation and results from Mendez and Losada (2004). The sensitivity of the model to the shape of the frequency spectrum, directional spreading and layer schematization are investigated. The model is then applied to field measurements by using a vegetation factor. This model has the ability to calculate two-dimensional wave dissipation over a vegetation field including some important aspects such as breaking and diffraction as used in SWAN model.