Trapping of water waves by pairs of submerged cylinders

This paper provides strong numerical evidence for the existence of two–dimensional trapped waves supported by a symmetrically arranged pair of submerged cylinders with a particular form of cross–section. Wide–spacing arguments applied to single submerged obstacles exhibiting zeros of transmission are used as the basis for seeking trapped waves. The integral equation technique developed for the scattering by arbitrary submerged obstacles in Porter (2001) is extended for this problem, and it is shown how trapped waves correspond to the point of intersection of two independently computed curves. Results are given for a variety of symmetrical pairs of submerged obstacles.