Water-wave interaction with submerged porous elastic disks
Siming Zheng, Michael H. Meylan, Deborah Greaves, Gregório Iglesias
Abstract
Hydroelastic interaction between water waves and submerged porous elastic disks of negligible thickness in water of finite depth is investigated under the assumption of small amplitude water-wave motion and structural response. The disks are either simply supported or clamped at their edges. Wave power can be absorbed/dissipated by the disks due to their porosity. A theoretical model based on the linear potential flow theory and eigenfunction matching method is developed to solve the wave scattering problem of the submerged disks. An indirect method, employing Kochin functions, is derived based on Green’s theorem to evaluate the wave power absorption/dissipation, and it produces accurate results at a lower computational cost than the conventional method. This theoretical model is applied to perform a multi-parameter study on the performance of a single submerged porous elastic disk, and an array of disks as well, particularly, in terms of near-field wave motion, disk deflection, far-field scattering coefficient, and wave power absorption/dissipation. Deploying multiple disks in an array is found to be a more promising approach for wave power absorption/dissipation compared to enlarging the area of a single disk.