Near Trapped Modes in Long Array of Truncated Circular Cylinders

Abstract

The purpose of this article is to investigate near trapped-mode occurrences by arrays of truncated cylinders. The basic question that this article tries to answer is whether near trapped modes (peak loading wave numbers) are indeed stimulated for arrays of truncated cylinders, such as in arrays of bottom-seated cylinders. Arrays of truncated cylinders are conceived as possible wave-energy-extraction mechanisms given that their modules are allowed to oscillate in surge (or sway) and heave, in contrast to bottom-seated cylinders, which are fixed. Hence, an additional question that should be answered is which actual mode of motion is important. To tackle these tasks, the governing hydrodynamic diffraction problem is considered. Different velocity potentials are defined for the liquid regions formed by the geometry of the truncated cylinders. The sought ultimate solution is achieved using the eigenfunction expansion technique combined with the direct approach, which, in contrast to the multiple-scattering method, is unquestionably more efficient and robust.