Bragg Scattering Phenomena by Multiple Asymmetric Trenches in a Two-Layer Fluid

Abstract Bragg scattering due to multiple asymmetric trenches in a two-layer fluid is explained in a framework of linear two-dimensional theory. Both fluids have finite depths. The upper fluid is confined by the free surface at the top, while the lower fluid is bounded below by an impermeable trench bottom. The fluid region is divided into subregions associated with the trench position. The solution of the boundary-value problem is analyzed by the matched eigenfunction method of water wave potential. The phase velocity and group velocity for both wave modes are derived from dispersion relations and analyzed graphically. By solving the boundary-value problem, the upper surface elevation, interface elevation, reflection, and transmission coefficients in surface and internal modes are obtained numerically. These results indicate that as the width and depth of the trenches increase, wave transmission diminishes, and the free surface elevation reduces as the incident wave passes over the trenches. The present model has significant importance to protect harbors and offshore structures by mitigating wave height displacement and transmission coefficients.