Water waves trapped by thin submerged cylinders: Exact solutions

Exact solutions of the linear water-wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise arbitrary) cross-section are constructed in the form of a convergent series in powers of the small parameter characterizing the “thinness” of the cylinder. The terms of this series are expressed through the solutions of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder.