Analysis of water wave scattering by a submerged perforated reef ball using multipole method

Based on linear potential theory, this study develops an analytical solution to water wave scattering by a submerged perforated reef ball. The series solutions for velocity potentials in the external and internal fluid domains of the perforated reef ball are developed using the multipole expansions and the separation of variables, respectively. The unknowns in the series solutions are determined by matching the porous boundary condition on the perforated reef ball. Also a numerical solution using three-dimensional multi-domain boundary element method (BEM) is developed. The special case of an impermeable reef ball is also examined. The calculation methods for the horizontal and vertical wave forces acting on the reef ball and the free surface elevation around the reef ball are given. The convergence of the calculation results is very rapid, and the results with five-figure accuracy are obtained using a few truncated terms in the series solution. The results by the analytical solution agree well with that by the multi-domain BEM solution. Typical calculation examples are presented to examine the effects of reef ball radius, porous effect parameter of reef ball and incident wave frequency on the wave forces and the free surface elevation. The results of analysis are valuable for engineering design and application of reef balls. The present analytical solution gives a new reliable benchmark for three-dimensional numerical models to wave interactions with perforated structures. Moreover, better understanding on wave scattering by perforated structures can be obtained during the analytically solving procedure.