Scattering of capillary-gravity waves by surface-piercing porous barriers in the presence of uniform current over a porous sea bed

Abstract

Capillary-gravity waves, influenced by both surface tension and gravity, interact strongly with marine structures, especially in the presence of uniform currents. Despite extensive studies on wave scattering by porous structures, the combined effects of surface tension, current, and porous barriers over a porous bottom remain insufficiently explored. This study examines the scattering of such waves by two thin surface-piercing porous barriers in the presence of a uniform current over a porous sea bed. A linear wave-structure interaction model is solved numerically through a hybrid Boundary Element-Finite Difference Method (BEM-FDM) and analytically through an eigenfunction expansion combined with a least-squares approach. The hybrid BEM-FDM efficiently handles higher-order boundary conditions that cannot be directly addressed by conventional BEM, while the analytical method eliminates the need for eigenfunction orthogonality and explicit mode coupling. The effects of surface tension, current velocity and direction, porous effect parameters of barriers as well as bottom, barrier length and spacing between them on reflection, transmission, and energy dissipation are analyzed. Results show that surface tension enhances reflection and dissipation while reducing transmission. Current direction strongly affects scattering: following currents enhance transmission, whereas opposing currents increase reflection and dissipation. Longer barriers and larger porous-effect parameters of both porous barriers and porous bottom enhance energy dissipation, while spacing between porous barriers induce interference driven oscillations.