Oblique water waves impacting on a thin porous wall with a partial-slipping boundary condition

Abstract

When an incoming water wave is parallel to a porous breakwater, a paradoxical phenomenon exists in that by strictly following the potential flow boundary condition of normal flux continuity on the interfaces, the water wave permeates the wall completely, regardless of breakwater porosity. To account for this paradoxical phenomenon when solving the problem of water waves obliquely impacting on a thin porous wall, a new partial-slipping boundary condition on the thin porous wall for potential flow is proposed. Analytical results show that when the water wave is parallel to a thin porous wall (i.e., the incident angle equals to 90°), the transmitted wave side remains quiescent, i.e., the transmitted wave side does not capture any wave energy when no viscous effect exists. This reveals that the above-mentioned paradoxical phenomenon disappears. The viscous boundary layer effect is also investigated in this study, which provides proper boundary conditions on a thin porous wall for viscous flows and detailed flow information.