Edge Waves Along Periodic Coastlines

The existence of edge waves travelling along a periodic coastline consisting of a straight and vertical cliff face from which protrudes an infinite number of identical thin barriers, each one extending throughout the water depth, is proved for sufficiently long barriers based on the linear theory of water waves. The water depth is assumed to be constant everywhere and for this reason these edge waves are fundamentally different from other edge waves known in water-wave theory which all rely on a varying bottom topography or a submerged obstacle for their support. The proof of existence uses the modified residue-calculus method and is constructive. The method provides a simple and efficient procedure for the determination of the trapped-mode frequencies.