Wave dissipation effects of a floating membrane

• Floating, flexible membranes experience significant wave-induced drift due to momentum changes caused by wave reflections. • Viscous damping can be captured effectively by modelling the membrane as a porous medium governed by Darcy’s law. • The classical Haskind relations are extended to include damping, offering generalized relations for porous structures. We investigate how a floating, flexible membrane dissipates wave energy and generates wave-induced forces by combining linear potential-flow theory with an elastic membrane model. The membrane is allowed to be porous, and viscous effects are incorporated through a Darcy-type resistance law. A full three-dimensional boundary-element formulation is developed to compute radiation and diffraction potentials, extended to include porous effects in the boundary conditions. This leads to generalized Haskind relations that remain valid in the presence of damping. The model captures both rigid-body motions and flexible deformation modes, allowing us to quantify their respective roles in wave-structure interaction. We show that flat membranes, despite their negligible thickness, experience significant mean drift forces due to momentum changes from reflected waves. Porosity introduces substantial damping, reducing modal response amplitudes while modifying the far-field scattering pattern and greatly influencing the drift force for both long and short waves. The numerical implementation is validated through energy-balance checks, convergence analyses, and agreement between multiple independent evaluations of excitation forces. These results provide new insights into the hydrodynamics of flexible, dissipative floating structures, relevant for applications such as floating solar islands, thin ice covers, and other flexible structures.