Wave diffraction from a small submerged circular cylinder in a slightly viscous fluid

Abstract

A simple solution for surface wave diffraction in a slightly viscous fluid, due to a submerged circular cylinder with restrained centre of mass, is given. The solution is asymptotic, valid in the limit where the cylinder radius tends to zero, in a fluid with small but finite viscosity. The solution is based on the dipole contribution to the Oseen solution for small Reynolds number flow past the cylinder. There is no wave reflection, just as in the conventional inviscid theory, but there is a positive phase shift, contrary to the phase delay predicted by inviscid theory. The magnitude of this phase shift is always considerably smaller than the absolute value of the corresponding negative phase shift according to inviscid theory.