Impact of Following Current Velocity on the Hydrodynamics of a Floating Permeable Flexible Membrane Breakwater near a Wall - Clémence Podgorny; Sarat Chandra Mohapatra; C. Guedes Soares (Journal of Marine Science and Engineering, 2026)
This paper presents a mathematical model to investigate how waves and currents interact with a flexible perforated floating membrane in finite water depth within the framework of linear wave theory. The perforated flexible membrane is modeled based on Darcy’s law and the one-dimensional string equation. The complex dispersion relation in the presence of current velocity is derived from the Green’s function technique using a fundamental source potential solution. The dispersion curve is analyzed by comparing the phase and group velocities for different water depths. Further, a physical model associated with the effect of current on a moored finite floating perforated flexible membrane integrated with a vertical wall is formulated. Then, the theoretical solution of a physical boundary value problem near a vertical rigid wall is obtained using the matching technique and the roots of the dispersion relation derived from the Green’s function technique. Numerical simulations are provided to verify the convergence of the series solution and the accuracy of the obtained analytical findings are evaluated against previously published analytical and experimental datasets. Further, several numerical results on the membrane deflection, hydrodynamic coefficients, and horizontal force on the wall for various structural parameters, mooring stiffness, and current velocities are analyzed. It is observed that the present analysis with this perforated membrane breakwater will be helpful to coastal and marine engineers to understand the influence of current velocity.