Hydrodynamic interactions between cnoidal waves and a concentric cylindrical structure with arc-shaped outer cylinder

Abstract

The interaction between cnoidal waves and a concentric cylindrical structure with an arc-shaped outer wall has been investigated theoretically using eigenfunction expansion approach. The arc-shaped outer cylinder is permeable and thin, protecting the porous dual-cylinder structure. Three cylinders are surface-piercing and rigidly installed on the flat bottom of an ocean. Analytical solutions were obtained based on the first approximation to cnoidal waves. A series of linear equations pertaining to unknown coefficients were solved using matching boundary conditions. Hydrodynamic forces on the cylinders and the diffracted wave faces around the cylinders were evaluated, and the effects of water depth, annular spacing, angle of incidence and structure configuration including the porosity parameter of the cylinders and the opening angle are illustrated via numerical results. The numerical results obtained for limiting cases agreed well with published results for a solid cylinder. The results indicated that the wave forces on the inner structure did not change significantly when the opening angle was greater than 2π∕3. The hydrodynamic loads on the inner cylinder of the concentric cylindrical structure were significantly lower than the wave force on a single cylinder. Moreover, the value of wave force on the inner cylinder of a concentric dual-cylinder structure with an arc-shaped outer wall was similar to that on the inner cylinder of a concentric two-cylinder system.