Interaction of Surface Gravity Waves on a Nonuniformly Periodic Seabed

The interaction of surface gravity waves on a nonuniformly periodic seabed is considered. The method of multiple scales is used to analyze the interaction leading to two coupled-mode equations. The power reflection coefficient is used as an indicator to evaluate the filter action of the bottom corrugation. The results show that the modes are strongly coupled when the Bragg resonant condition is satisfied. The characteristics of the filtration are found to be enhanced by imposing special types of amplitude and phase modulated periodic nonuniformities, including amplitude taper and chirped periodic variations.