Interaction of water waves with three-dimensional periodic topography (Q2731199)

This paper uses linearized theory to examine the scattering and trapping of water waves by a three-dimensional submerged topography, infinite and periodic in one horizontal coordinate and of finite extent in the other. Two problems are considered, one being the scattering by the topography of parallel-crested obliquely incident waves, and the other the propagation and trapping of modes along the periodic topography. It is found that trapped waves can exist over any periodic topography which is sufficiently elevated above the unperturbed bed level, and fundamental differences are established between trapped waves and the analogous Rayleigh-Bloch waves which exist on periodic gratings in acoustic theory. Computational results show that for the scattering problem there exist zeros of transmission at discrete wavenumbers for any bed elevation and for all incident wave angles.