Wave Scattering and Trapping by C-Type Floating Breakwaters in the Presence of Bottom-Standing Perforated Semicircular Humps

In this paper, the propagation of surface gravity waves over multiple bottom-standing porous semicircular humps is examined in the absence and presence of double floating C-type detached asymmetric breakwaters. Both wave scattering and trapping phenomena are investigated within the framework of small-amplitude linear water wave theory, with the governing problem numerically solved using the multi-domain Boundary Element Method (BEM) in finite-depth water. A detailed parametric analysis is conducted to evaluate the effects of key physical parameters, including hump radius, porosity, spacing between adjacent humps, and the separation between the two C-type detached breakwaters. The study presents results for reflection and transmission coefficients, free-surface elevations, and the horizontal and vertical forces acting on the first perforated semicircular hump, as well as on the shore-fixed wall. The findings highlight the significant role of porous humps in altering Bragg scattering characteristics. For larger wavenumbers, wave reflection increases notably in the presence of a vertical shore-fixed wall, while it tends to vanish in its absence. Reflection is also observed to decrease with an increase in semicircle radius. Furthermore, as the wavenumber approaches zero, the vertical force on multiple permeable semicircles converges to zero, whereas for impermeable semicircles, it approaches unity. In addition, the horizontal force acting on the shore-fixed wall diminishes rapidly with increasing porosity of the semicircular humps.