Estimation of wall effects on floating cylinders

Under the assumptions of classical linearised water-wave theory, the time-harmonic two-dimensional motion of a rigid body floating in the surface of a fluid may be characterised by various coefficients which express components of the hydrodynamic forces acting on that body. For a single body in isolation, these are relatively simple to calculate. For bodies placed next to a vertical wall, the corresponding calculations are often much more complicated. In this paper the well-known wide-spacing approximation is used to develop approximations to the hydrodynamic coefficients for a body having a vertical plane of symmetry, but otherwise of arbitrary cross-section, next to a wall solely in terms of the results for an isolated body. Exact results are compared with the wide-spacing approximations for semi-immersed circular cylinders and cylinders of rectangular cross-section. They show that the approximation works remarkably well over all frequency ranges and even when the cylinders are very close to the wall.