Analytical study of water wave interaction with a vertical cylinder surrounded by a non-concentric cylindrical perforated wall

The wave interaction between water waves and concentric cylindrical structures received extensive attention, but analytical investigations on the hydrodynamic problems of non-concentric structures were rarely reported. In this study, a vertical cylinder surrounded by a non-concentric cylindrical perforated wall is taken as an example, where the vertical cylinder can be regarded as a platform and the perforated wall can serve as a protective facility. An analytical method for the hydrodynamic problems of non-concentric cylindrical structures is developed in the context of the potential flow theory. In the analytical process, the entire fluid domain is divided into two regions, and the velocity potentials of the fluid motion are expressed by the Bessel–Fourier series. Graft's addition theorem is used to address the problem caused by hybrid coordinate systems, and the expansion coefficients in the velocity potentials are determined through the boundary condition on the perforated wall. The linear wave forces and mean drift forces on the cylinder and the perforated wall are obtained, and the calculation expression of the dissipated wave power of the perforated wall is given. The analytical solution converges rapidly, and the calculated results are consistent with the numerical results of the boundary element method. Typical examples are presented to examine the effects of the wave frequency, the cylinder position, and the porous effect parameter on the hydrodynamic quantities. The results show that the wave forces on the inner cylinder and the perforated wall are sensitive to the cylinder position, and there exists an optimal geometric porosity to maximize the energy-dissipating performance of the perforated wall. The present analytical scheme can provide a basic reference for wave-induced hydrodynamic problems of other complicated non-concentric structures.