Wave radiation and diffraction from a small submerged circular cylinder

The linear water wave radiation/diffraction problem for a small submerged cylinder is solved analytically in terms of an asymptotic expansion. The expansion parameter is the radius of the cylinder divided by its depth of submergence. The influence of the cylinder on the wave field is represented by a rotating dipole, which obeys the free-surface conditions and radiation conditions. Our results agree fully with the classical results. We find a basic physical reason why the circular shape is exceptional compared to all other obstacle geometries: it is because of the circular paths of fluid particles in free linear deep-water waves.