Trapped modes in an axisymmetric water-wave problem

Trapped-mode solutions, that is, examples of non-uniqueness, are given for a class of axisymmetric problems in the linearized theory of the interaction of water waves with structures. The solutions are constructed by placing an axisymmetric ring source in the free surface with the radius of the ring chosen to eliminate radial circular waves. The ring-source potential then corresponds to a localized standing wave. Suitable structural surfaces are obtained by looking for stream surfaces of the flow.