Oblique Water-Wave Scattering by Two Thick Submerged-Horizontal Plates in a Two-Layer Fluid

Abstract

This paper analyzes the problem of oblique water-wave scattering by two thick submerged-horizontal plates in a two-layer fluid. The analysis is based on the small-amplitude water-wave theory in water of finite depth. The solution of the associated boundary value problem was derived through the matched eigenfunction expansion method. Numerical results for the reflection energies of surface and internal waves were computed and analyzed in various configurations. The effects of the geometrical parameters—the submergence, thickness, and length of the submerged plates, and the distance between them—on the reflection energies in surface and internal modes (SM and IM, respectively) are discussed in detail. The study shows that, when the interface lies between the two plates, the largest reflection energies are found in both modes. The numerical results were compared with those available in the literature, and were found to be in good agreement. The energy relation was also derived, and the numerical results were found to satisfy this relation accurately.