A BEM model for wave forces on structures with thin porous elements

A boundary element method (BEM) model is presented for wave forces on structures composed of solid and porous surfaces, where the porous surface can be subject to either a linear or quadratic pressure–velocity relation. In the case of the quadratic relation, the solutions to the radiation and diffraction problems cannot be superimposed to obtain a solution for body motions in waves. Instead, a solution method is proposed which solves for the motion response and wave forces on the body simultaneously. Solutions for the radiation and diffraction problems are then obtained as special cases. Hydrodynamic identities and expressions for the mean drift force for combined solid-porous bodies are also derived. It is shown that in the case of a quadratic pressure drop, the hydrodynamic coefficients are no longer symmetric and the Haskind relation must be modified to account for the pressure drop across the porous surface. The BEM solution is verified against an analytical calculations and results for the excitation and mean drift forces are shown to agree well. A case study is presented for a floating truncated cylinder, with a concentric porous outer cylinder. It is shown that the porous outer cylinder significantly increases the damping at low frequencies, where wave radiation damping is low, leading to a lower motion response.