Surface gravity wave interaction with a partial porous breakwater in a two-layer ocean having bottom undulations

Linear surface gravity wave scattering by a partial porous breakwater is studied in a two-layer ocean having an interface with bottom undulations. The partial breakwaters, namely surface-piercing breakwater (SPB) and bottom-standing breakwater (BSB), are considered. The continuity of fluid pressure and mass flux is applied at interface boundaries, while mass conserving conditions are employed to account for slope discontinuity in seabed geometry. Porous breakwaters' reflective and dissipative characteristics are studied under wave-wave interaction. The study reveals that when a mound bottom is present, more incident waves in interface mode are transmitted through BSB, while more waves in surface mode are dissipated. More incident waves in surface mode are transmitted through SPB, while more waves in interface mode are dissipated. In contrast, more transmission occurs in surface mode through both BSB and SPB for a slope-shelf bottom. However, the breakwater dissipates a substantial amount of incident-wave energy in interface mode. Further, a considerable reduction in wave transmission occurs due to higher reflection by the interface-piercing porous breakwaters, and the breakwaters experience high wave loads. Relatively, porous breakwater dissipates less wave energy in shallow depth. The study reveals that the dead water effect is weakened by the porous breakwater.