An example of non–uniqueness in the two–dimensional linear water–wave problem involving a submerged body

The non–uniqueness of the two–dimensional linearized water–wave problem was recently proved by McIver, who showed that there exist localized fluid motions between particular pairs of partly immersed cylinder sections. In this paper it is shown how further examples of non–uniqueness can be constructed which include the presence of a submerged circular cylindrical section in addition to a pair of surface cylindrical sections. Further examples involving non–circular sections are also presented.