Bragg Scattering of Surface Gravity Waves by an Array of Surface-Piercing Variable Porosity Barriers

Abstract

The scattering of gravity waves by vertically staggered multiple porous barriers having variable porosity is analyzed within the framework of linearized water wave theory in two dimensions. The barriers are assumed to follow quadratic pressure boundary conditions to account for energy dissipation with the changes in the wave height, which is often neglected in the case of Darcy’s law. A generalized code based on the dual boundary element method (DBEM) is developed for solving the boundary value problem. Three different wave barrier configurations are considered with the same volume of materials required for its construction to identify the best-performing barriers. The hydrodynamic performance of the barriers with progressively decreasing porosity is found to be better than the barriers with gradually increasing porosity or barriers with constant porosity. The scattering coefficients attain optimal at integer multiples of half the wavelength. It is appropriate to select relative spacing in the range of 0.2–0.3 for better hydrodynamic performance for any field design condition. For deeper water depths (k0h > π), increasing the relative submergence depth beyond 0.2 is insignificant to the change in hydrodynamic performance. For the practical field range of k0h and for a threshold wave transmission coefficient of 0.2, the appropriate relative submergence depth is 0.6. The results of this study would help in the hydrodynamic design of a progressive wave absorber.