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

Abstract

In this paper, we employ the addition theorem and superposition technique to examine the trapped mode of water wave problems. The scattering of water waves by arrays of vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary free of principalvalue calculation using bump contour owing 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. The physical-resonance phenomena of near-trapped modes are our concern. Several examples are given to demonstrate the validity of the proposed approach.