The oblique wave trapping by bottom-standing semi-circular porous structures with finite widths positioned finitely apart from a vertical partially reflecting seawall under the influence of ocean uniform current is the subject of the present research. The problem is analyzed based on the small-amplitude water wave theory in water of finite depth, using the Sollitt and Cross model (1972) for wave motion within the porous structure. Using a constant boundary-element method based numerical technique, the corresponding boundary value problem's solutions are achieved numerically. The boundary value problem is transformed into integral equations over the physical boundaries using the boundary-element method. The system of linear algebraic equations is obtained by discretizing the physical boundaries into a finite number of elements. The effect of ocean current on the wave energy reflection coefficients, wave energy dissipation and the hydrodynamic forces are used to analyze different elements of structural configurations in oblique wave trapping. Proper combinations of the vertical partially reflecting seawall and porous structure can offer long-term, economically viable solutions to defend different marine structures from wave attack.
Researchers have developed impermeable breakwaters to defend coastlines and coastal infrastructure from wave attacks. These breakwaters span through the water depth (Abul-Azm, and Williams, 1997, Mondal and Alam, 2018), floating on the top (Söylemez and Gören, 2003), and submerged at intermediate depths (Zheng, 2007, Mondal and Takagi 2019). These breakwaters act as a buffer zone by reflecting wave energy. Porous breakwaters, on the other hand, create a shelter zone through wave energy reflection and absorption mechanisms. Many researchers evaluated the influence of porous breakwaters on wave energy dissipation using both an analytical (Liu and Li, 2013) and experimental technique (Chyon, 2017, Shen, 2022). Many theoretical and numerical investigations of thick porous structures placed on rigid and porous seafloors, as well as surface-piercing structures, have been conducted in recent decades using linear water wave theory. The first model for wave-induced flow in a porous material was developed by Sollit and Cross (1972). In order to provide numerical solutions to such scattering problems, Sulisz (1985) presented the boundary element methodology into account for different types of rubble-mound breakwaters, which serve as a good model of most prevalent porous structures. Dalrymple (1991) and Madsen (1974) then presented a research on the transmission and reflection of oblique incident waves in the presence of porous structures of indeterminate length. Zhu (2001), Rambabu and Mani (2005), and Twu et al. (2002) used semi-analytical and computational methodologies to examine the wave diffraction and damping properties of porous breakwaters with different shapes and structural arrangements placed over uniform and undulating seabed. According to these findings, wave energy dissipation increases with structural thickness until it reaches a maximum value determined by porosity and friction coefficient. The results also highlight the fact that when a breakwater's height is almost half of the overall depth, it can reduce wave transmission by almost 55%. According to a report, a porous structure that penetrates the surface can act as a wave-trapping device more successfully than a bottom-standing one. However, in order to investigate the effect of the porosity of the fully-extended and submerged breakwaters on the non-breaking wave transformations, Koley et al. (2020) conducted experimental studies. It has been demonstrated that waves passing through a submerged porous structure produce higher harmonic waves, and that the dissipation of higher harmonic waves is more significantly impacted by porosity than that of the primary wave.