Abstract
Semi-analytical solutions are proposed to investigate the effects of a submerged/suspended circular patch on water waves scattering. The patch is simplified to periodic cylindrical lattices with a strong contrast between the cylinder spacing and the typical wavelength. The homogenization theory is employed to derive the effective equations on the macro-scale (wavelength), in which the constitutive coefficients are obtained by numerically solving the micro-scale (cylinder spacing) problem in a unit cell. To simulate the turbulence in the circular cylinder patch, a bulk eddy viscosity model is applied through balancing the time-averaged energy over a wave period. Eigenfunction expansions method is used to solve the macro-scale problem, where a complex frequency dispersion relation is solved by the multiple successive approximation technique. Comparisons between the laboratory measurements and the waves/submerged circular patch model results show acceptable agreements for small amplitude waves. The waves/suspended circular patch model is not checked experimentally due to the lack of data. However, this suspended patch model is shown to reproduce the results of wave/emergent circle forest problem. A comprehensive comparison between the submerged, suspended and emergent circular patches on wave scattering is also presented.
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