Wave scattering by porous cylinders with inner columns near a vertical wall

Abstract

This paper studies wave scattering by multiple dual porous circular cylinders in front of a vertical wall. Each cylinder is composed of an outer partially perforated cylindrical shell and an inner impermeable column, and a circular wave-absorbing chamber is formed by the shell and column. An analytical solution to the hydrodynamic problem is developed in the context of potential flow theory. In the solving procedure, the hydrodynamic problem is transformed into an equivalent problem in an open water domain by using the image principle. The whole fluid domain in the equivalent problem is divided into multiple regions, and the velocity potential of the fluid motion in each region is expressed as the Fourier–Bessel series. The effect of the perforated shell on wave motion is considered through a pressure loss condition. The unknown coefficients in the velocity potential are determined by the transmission conditions on the boundaries between adjacent regions. The wave force, wave run-up on the porous cylinders, and the surface elevation near the cylinders are calculated. The analytical results are consistent with published results in several limiting cases. Typical cases are presented to clarify the characteristics of the wave force and wave run-up on the cylinders and discuss the effects of the wall and hydrodynamic interference on the hydrodynamic quantities. Moreover, several feasible applications of dual porous cylinders are discussed by visualizing the distribution of wave amplitude near the structures, and some valuable results are given.