Wave interaction with an array of porous walls in a two-layer ocean of varying bottom topography

Abstract

Oblique wave scattering by a breakwater consisting of an array of thin porous walls in a two-layer ocean with varying bottom topography is investigated by using linear wave theory. Further, wave trapping is studied by considering an impermeable seawall. The entire bottom profile is assumed to be a shelf-type comprising a varying bottom of finite length and two uniform bottoms of semi-infinite lengths. Porous walls extending from bottom to free-surface are assumed at a lower water-depth level (lee side). Impingement of waves, which approach from a deeper depth level (seaside), on walls is considered. The Fourier method or method of eigenfunction expansion is applied for the uniform bottom, whereas an approximation technique, called a mild-slope equation, is used for the varying bottom. Solutions from these two methods are matched at interfaces under physical conditions. An explicit solution is derived in the form of a system of algebraic equations. The effect of several bottom configurations on wave interaction with porous walls is analyzed. Reflection and transmission coefficients and wave force on porous walls and seawall are analyzed for the parameters related to waves, bottom, and porous medium. The study reveals that porous walls are very effective in reducing wave transmission for bottom profiles dominated by waves. Wave forces on porous walls are less in the two-layer ocean than in a homogeneous ocean. In wave trapping, seawall attains higher wave-force for incoming surface waves than for incoming interfacial waves. The ratio of water-depth levels and wave incident angles are also analyzed for the mitigation of wave forces. The force on seawall increases with the increased depth ratio in surface wave incidence, while the force decreases with the increased depth ratio in interface wave incidence. The findings may be useful for coastal engineers to understand wave scattering by multiple porous structures in the stratified ocean.