Analytical and experimental studies on Bragg scattering of water waves by multiple submerged perforated semi-circular breakwaters

This study develops analytical solutions for Bragg scattering of water waves propagating over a series of submerged perforated semi-circular breakwaters (bars) based on potential theory. The series solutions for velocity potentials in the external common fluid domain of the bars are expressed through multipole expansions, whilst those in the internal fluid domains are given using the separation of variables. The continuous condition of fluid velocity and a quadratic pressure drop condition on the perforated semi-circular arcs are applied to determine the unknowns in the series solutions. In the analytical solutions, obliquely and normally incident waves are independently considered. The calculation methods of the reflection, transmission and energy loss coefficients are given. Experimental tests are performed to measure the reflection and transmission coefficients of the breakwaters at different wave periods and water depths. The analytical solutions are in excellent agreement with the independently developed multi-domain BEM (boundary element method) solutions, and are also compared with the wide-spacing approximations and the experimental results. Calculation examples are presented to check the effects of various parameters (e.g., bar number, bar radius, bar spacing and incident wave angle) on the hydrodynamic quantities of the breakwaters. Main valuable results for engineering application are draw.