Hydrodynamics and near trapping effects in arrays of multiple elliptical cylinders in waves

Abstract

The purpose of the present study is the investigation of the hydrodynamic interactions induced by arrays of elliptical cylinders subjected to regular waves. The solution methodology employs linear potential theory and is based on pure analytic considerations. The interaction phenomena are approached using the Mathieu functions addition theorem which converts elliptical harmonics from one elliptic coordinate system to a remote elliptic coordinate system. The followed approach resembles the ‘direct’ solution methodology which is used for the analytical solution of the diffraction problem by arrays of circular cylinders. The ‘direct’ approach allows, among others, the construction of a linear matrix equation for the calculation of the expansion coefficients of the diffraction component(s) which accordingly is used to trace the wavenumber(s) under which trapped modes may be stimulated to induce wave trapping in the array, and reduction of the energy radiated to the far-field. The numerous computations which are performed, specifically verify that any array of elliptical cylinders, in accord with arrays of circular cylinders, is potentially a wave trapping configuration, which is connected mainly i) with sharp amplifications in all modes of hydrodynamic loading (both forces and moments) and ii) strong free-surface elevations in the liquid regions between the cylinders and on the cylinders' surfaces accordingly.