Oblique Long Wave Scattering by an Array of Bottom-Standing Non-Smooth Breakwaters

Abstract

Bragg scattering of surface gravity waves by an array of submerged bottom-standing non-smooth breakwaters is studied under the assumption of linearized long wave theory. The closed-form long-wave analytical solutions are derived and validated by comparing them with the results available in the literature. The role of various physical parameters such as breakwaters friction coefficient, depth, width and gap between the adjacent breakwaters are investigated by analyzing the reflection and transmission coefficients. Further, the time-domain simulation for the scattering of long gravity waves over multiple breakwaters is analysed for different values of parameters of breakwaters. The results reveal that the rough surface of the breakwater plays a vital role in reducing wave reflection and transmission. Moreover, it is observed that the transmitted wave dissipates completely for larger values of friction parameters. For certain critical angles, change in wave dissipation becomes maximum due to the variation of phase of the incident wave. Various findings can be considered as benchmark results for the design of the non-smooth structures to attenuate the waves based on the Bragg reflection.

Keywords

• bottom-standing structures
• bottom-friction
• shallow water equations
• Bragg reflection
• free surface elevation