A semi-analytical theory for water waves interacting with a submerged/suspended circular cylinder patch. (1st March 2022) - Hu, Jie; Lin, Y.H.; Maza, Maria
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. Highlights: Semi-analytical solutions are presented for water waves scattering by a submerged/suspended circular patch as the main creatively work of this study. The present solutions have been checked with laboratory measurements and other solutions from previous studies. The solutions are simple and allow straightforward numerical implementations. No additional fitting coefficient is needed in the model computation. A comprehensive analysis on wave scattering by different forms of circular patches has been discussed.