Water Waves on Flexible and Porous Breakwaters

Abstract

This is a theoretical study of the reflection and transmission of small‐amplitude waves by a flexible, porous, and thin beam‐like breakwater held fixed in the seabed. The fluid motion is idealized as a linearized, two‐dimensional potential flow and the breakwater is idealized as a one‐dimensional beam of uniform flexural rigidity and uniform mass per unit length. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free‐surface elevation, hydrodynamic force acting on the breakwater, and the overturning moment are determined. The dynamic response of the breakwater in terms of bending moment and shear force are also evaluated. It is found in general that hydrodynamic force increases as structural rigidity increases. The magnitude of the force is reduced dramatically for a stiffer porous breakwater. It is also shown that the stiffer structures deflect in the first mode, whereas the structures with large flexibility oscillate in higher modes. The reflection and transmission coefficients at different rigidity and porosity of a breakwater are analyzed. Results are presented to illustrate the effects of the various waves, structural parameters, and porosity parameters on the response and efficiency of the breakwater.