Analysis of water wave interaction with multiple submerged porous reef balls

This paper investigates the interaction of water waves with a group of submerged porous reef balls, which are hemispheres with centers lying on a plane seabed. An analytical solution based on potential theory is developed. In the solving process, the series solutions of the velocity potentials in the exterior and internal fluid domains of the reef balls are obtained by means of multipole expansions and separation of variables, respectively. The unknown expansion coefficients in the velocity potentials are determined by matching the porous boundary condition on the surface of each reef ball, where the vital point is the shift of multipoles among different local spherical coordinate systems. The special case of multiple impermeable reef balls is also considered. The wave forces in the sway, surge, and heave directions acting on the reef balls as well as the surface elevation near the structures are calculated. The predictions of the analytical solution are in excellent agreement with the numerical results of an independently developed three-dimensional multidomain boundary-element method solution. Case studies show that the hydrodynamic interaction is obvious only when reef balls are very close. Moreover, the feasibility of the submerged porous breakwaters composed of a series of porous reef balls with appropriate arrangements is examined.