Trapping and near-trapping by arrays of porous cylinders in water waves using the addition theorem and superposition technique

Abstract

Following the successful experiences of solving water-wave scattering problems for multiple impermeable cylinders, we extend the null-field integral formulation to deal with the problems of surface-piercing porous cylinders in this paper. The null-field integral equations in conjunction with the addition theorem and Fourier series are employed to solve the water-wave problem. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values thanks to the introduction of degenerate kernels for fundamental solutions. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. It is found that the disorder is more sensitive to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those by using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those in the literature.