Water wave scattering by dense or sparse arrays of surface-piercing bodies by integral matching method

In this work, integral matching method is used for the numerical study of water wave scattering by arrays of surface-piercing structures. Such a method, already used for many years for rectangular breakwaters, is applied to structures of various shapes, including arrays of vertical cylinders, for which the contour of vertical boundaries is discretized into steps. Finite width channels of constant depth are considered, which may also correspond to uneven periodic structures along the transverse direction. Applications to sparse or dense arrays of vertical cylinders are discussed. For sparse cylinders, first order and higher order Bragg resonance are observed in both the incoming wave direction and other directions for the higher frequencies. For dense cylinders, considered as porous media, dispersion relation for the wave within the cylinders arrays is discussed through interference process due to the finite length of the porous medium (or the cylinders array) along the incoming wave direction. It is found that the wavelength slightly depends on the cylinders arrangement at given porosity and specific surface.