Wave diffraction by a long array of cylinders

TLDR

Water wave diffraction by an array of bottom‑mounted circular cylinders is analyzed under linear theory, showing that near‑resonant modes can arise between adjacent cylinders at critical wavenumbers and are linked to trapped waves in a channel. The array consists of identical, equally spaced cylinders. When the array contains many but finite cylinders, near‑resonant modes between adjacent cylinders at critical wavenumbers produce unusually large loads, and a second trapped wave with Dirichlet boundary conditions on the channel walls, as well as higher‑wavenumber nearly trapped modes, is also observed.

Abstract

Water wave diffraction by an array of bottom-mounted circular cylinders is analysed under the assumptions of linear theory. The cylinders are identical, and equally spaced along the array. When the number of cylinders is large, but finite, near-resonant modes occur between adjacent cylinders at critical wavenumbers, and cause unusually large loads on each element of the array. These modes are associated with the existence of homogeneous solutions for the diffraction by an array which extends to infinity in both directions. This phenomenon is related to the existence of trapped waves in a channel. A second trapped wave is established, corresponding to Dirichlet boundary conditions on the channel walls, as well as a sequence of higher wavenumbers where ‘nearly trapped’ modes exist.