The scattering of regular surface waves by a fixed, half-immersed, circular cylinder

Abstract

A train of regular surface waves is incident upon a fixed, half-immersed, circular cylinder; the waves are partially reflected and partially transmitted, and also induce hydrodynamic forces on the cylinder. In order to give a theoretical study of this problem, we make the familiar assumptions of classical hydrodynamics and then solve the linear, two-dimensional, diffraction boundary-value problem, using Ursell's multipole method. Accurate numerical results are presented (in the form of tables) for four important (complex) quantities; these are the reflection and transmission coefficients, and two dimensionless coefficients which describe the horizontal and vertical forces on the cylinder. We have also made an experimental study, in which we measured the forces on the cylinder, and the reflection coefficient. These measurements are compared with the linear theory, and also with other experimental data; discrepancies are noted and an attempt to analyse them is made. We have also measured the mean horizontal forces on the cylinder; these results are compared with the predictions of a simple formula obtained by Longuet-Higgins.