In this paper the diffraction of a plane first-order solitary wave by a vertical permeable breakwater with calculation of the wave loading is investigated. The interaction between long non-linear water waves and dissipative/absorbing coastal structures that are commonly used in coastal engineering is investigated using both analytical and numerical technique. The breakwater consists of a vertical permeable surface-piercing elliptical cylinder fixed in the ground. The analytical model herein is based on the application of Boussinesq equations to describe the diffraction of the first-order solitary wave by an elliptical breakwater. The method of solution is based on perturbation theory, using a perturbation parameter defined in terms of surface geometry of the cylinder. The analysis includes terms up to the first-order in this parameter, where the zeroth-order solution corresponds to a circular cylinder. The velocity potentials at the zeroth and first orders are expressed as eigenfunction expansion involving unknown coefficients that are determined through the boundary conditions on unperturbed cylinder. The flow through the porous breakwater is assumed to obey Darcy’s law. The total force onto the elliptical cylinder is obtained by integration of the pressure over permeable cylindrical wall. The analytical solution is obtained by means of a Fourier transformation technique. The effects of porosity, relative wave length and the incident wave angle are discussed. Numerical results compare well with previous predictions for the limiting cases of a permeable cylindrical breakwater.

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