The interaction of waves with arrays of vertical circular cylinders

TLDR

The scattering of water waves by an array of N bottom‑mounted vertical circular cylinders is solved exactly using the Spring & Monkmeyer 1974 method, with comparisons to the McIver & Evans 1984 approximation and an analysis of the long‑wave limit for two equal cylinders. A major simplification of the theory allows easier evaluation of forces, providing new formulae for first‑ and mean second‑order forces and for the free‑surface elevation near a cylinder.

Abstract

The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.