A semi-analytical study of oblique wave interaction with two $\boldsymbol {\sqcap }$-shaped breakwater designs—floating and bottom-fixed structures—incorporating two thin porous plates is presented using linearized theory. Wave potential for both configurations is developed using the eigenfunction expansion method, considering both progressive and evanescent wave modes. The problem of oblique wave scattering by $\boldsymbol {\sqcap }$-shaped breakwaters is reduced to a set of coupled integral equations of first kind, based on horizontal velocity components. These equations are solved using the multi-term Galerkin approximation with appropriate basis functions to handle the square-root singularities at sharp edges of the porous barriers. The performance of the models is evaluated by examining reflection, transmission and energy dissipation coefficients, along with free surface elevation and horizontal drift force. We observe that increasing the plate length of the breakwaters attenuates the incident waves more effectively than increasing the width. Additionally, the floating $\boldsymbol {\sqcap }$-shaped breakwater significantly reduces the free surface elevation in the transmitted region. The results from the developed model can provide valuable insights for the design of wave–structure systems in shallow waters.

The problem of oblique wave scattering by a rectangular submarine trench is investigated assuming a linearized theory of water waves. Due to the geometrical symmetry of the rectangular trench about the central line $x=0$, the boundary value problem is split into two separate problems involving the symmetric and antisymmetric potential functions. A multi-term Galerkin approximation involving ultra-spherical Gegenbauer polynomials is employed to solve the first-kind integral equations arising in the mathematical analysis of the problem. The reflection and transmission coefficients are computed numerically for various values of different parameters and different angles of incidence of the wave train. The coefficients are depicted graphically against the wave number for different situations. Some curves for these coefficients available in the literature and obtained by different methods are recovered.