Surface Gravity Wave Interaction with a Partial Porous Breakwater in the Presence of Bottom Undulation

Abstract

Using potential flow theory, oblique wave scattering and trapping by a partial porous breakwater having finite width are studied under the assumption of small-amplitude water wave theory in the presence of seabed undulation. This study is performed for regular incident waves that approach from deeper water depth and impinge on the porous breakwater at lower water depth. The two constant levels of deeper and lower bottoms are linked by a smooth arbitrary bottom topography, which may be regarded as a continental slope. In the lower-depth water, two types of porous breakwaters, namely, bottom-standing and surface-piercing breakwaters, are considered with and without a seawall. The analytical method of eigenfunction expansion is adopted for constant water depth, whereas an approximate method of the modified mild-slope equation is employed for varying water depth. Different bottom configurations are applied in this study. Reflection and transmission coefficients of waves and wave force on seawall are calculated for various physical parameters related to porous breakwater and waves. The role of seabed undulation on wave scattering and trapping is analyzed. The effectiveness of the breakwater is studied from the reflection and transmission coefficients. Results show a major difference in breakwater’s performance in scattering and dissipating waves under the condition of varying water depth compared to the case of constant depth of water. The tranquillity zone is obtained by optimizing various physical parameters. This study provides some theoretical knowledge related to wave interaction with partial porous structures under varying water-depth conditions. Moreover, it finds engineering applications concerned with the creation of tranquility regions and the protection of seawall.