Oblique Wave Scattering by a Pair of Asymmetric Inverse $Π$-Shaped Breakwater

The topic of wave scattering by different breakwaters has unfolded over the past few decades, largely driven by the profound impacts of global climate change. In this study, a completely new type of breakwater, inverse $Π$-shaped breakwater, has been taken into account for serving both purposes from analytical as well as an application point of view. During the formulation, the actual physical problem is transferred into a boundary value problem by employing the small amplitude water wave theory. With the aid of eigenfunction expansion, the problem is reduced to a set of integral equations having square-root singularities at the submerged edges of thin structures. To address such singularities, a multi-term Galerkin approximation technique is used along with Chebyshev polynomials (multiplied with suitable weights) as basis functions. The numerical methodology employed here validates with different previous literatures as special cases. Then, numerical solutions of the reflection and transmission coefficients, hydrodynamic forces are graphically illustrated across various dimensionless structural parameters. In summary, the present paper offers valuable insights into the dynamics of wave scattering by a pair of asymmetric inverse bottom-mounted $Π$-shaped breakwater, emphasizing the role of different non-dimensional parameters in this system.