Analysis of water wave interaction with a submerged fluid-filled semi-circular membrane breakwater

Abstract

This study investigates the hydroelastic interaction between water waves and a submerged fluid-filled semi-circular membrane breakwater based on potential theory. An analytical solution for wave interaction with the membrane breakwater is developed. The series solutions for velocity potentials in the external and internal fluid domains of the breakwater are obtained using the multipole expansions and the separation of variables, respectively. The unknowns in the series solutions are determined by the boundary conditions on the surface and at the two ends of the semi-circular membrane. In addition, a numerical solution for wave interaction with a submerged fluid-filled circular-arc membrane breakwater is developed using the multi-domain boundary element method (BEM). In the numerical solution, the boundary condition on the membrane's surface is directly discretized by expressing the membrane deflection as an integral representation involving the unknown dynamic pressure jump across the membrane. The calculation results from the present analytical solution and the numerical solution are in good agreement. The present numerical results also show reasonable agreement with the numerical and experimental results in literature. Calculation examples are presented to examine the basic features of the hydrodynamic quantities (reflection and transmission coefficients, wave surface elevation and membrane deflection) for the fluid-filled membrane breakwater. Valuable results are given for the engineering design.