Wave Energy Dissipation by Multiple Permeable Barriers in Finite Depth Water

A wave energy dissipation problem is solved for multiple permeable barriers in the water of finite depth. Applying Havelock's inversion formulae, this problem reduces to a set of first kind Fredholm integral equations involving potential differences across the barriers. The methodology utilized in this study is multi-term Galerkin's technique with a set of basis functions involving Chebychev's polynomials. A linear system has been solved for numerical estimations of the transmission and reflection coefficients. Dynamic wave force and wave energy dissipation have been computed both analytically and numerically. Also, at the end of the permeable barriers, square-root singularity of fluid velocity is tactfully handled. The numerical results for wave energy dissipation, dynamic wave force and reflection coefficients are depicted against wave numbers considering various values of parameters. Excellent ratification between previous results in the literature and present results is demonstrated.