The scattering of water waves by an array of circular cylinders in a channel

The full linear problem of the scattering of water waves by an array of N bottom-mounted vertical circular cylinders situated in a channel of constant depth and width is solved using the method of multipoles. A simple formula is derived for the velocity potential in the vicinity of a cylinder, and in particular on the cylinder surfaces, which allows hydrodynamic quantities such as forces to be easily evaluated. The simplicity of the solution makes the evaluation of quantities of interest straightforward and extensive results are given. An approximate solution for the forces on the cylinders, based on the assumption that the wavelength of the incident wave is long compared with the cylinder radii, is also given, and this is compared with results from the exact linear solution.