Diffraction by a gap in an infinite permeable breakwater

The linearized theory of water waves is used to study the diffraction of an incident wave by a gap in a permeable breakwater. Under the assumption that the wavelength is much greater than the thickness, the breakwater is replaced by a thin barrier and a suitable boundary condition applied on the barrier to model the permeability. A new Green’s function is used in an application of Green’s theorem to obtain an integral equation which is solved numerically to obtain the flow field. An approximate solution valid for large gaps is also given. Results are presented to illustrate the effects of permeability and changes in the angle of wave incidence.