Diffraction of water waves by a segmented permeable breakwater

The linearized theory of water waves is used to examine the diffraction of an incident wave by a permeable breakwater that consists of a number of distinct elements. Under the assumption that the wavelength is much greater than the thickness, each element is replaced by a thin structure and the permeability is modeled by a suitable boundary condition applied on its surface. The diffracted wave field is obtained by the solution of an integral equation and results are presented to illustrate the effects of permeability and of the characteristics of the incident wave. Introduction Many beaches throughout the world are protected by a breakwater that is made up of a line of separated elements that are parallel to the shore (see King et al. 2000, Thomalla and Vincent 2003, and the references therein). The present work provides a simplified method for the calculation of the wave field around such a “segmented breakwater” that is made up of a number of distinct elements. The elements are assumed to be permeable, to stand in water of constant depth, and the wavelength of the incident waves is taken to be much greater than the thickness of the breakwaters so that each may be modelled by a thin vertical structure. With these assumptions the depth dependence can be factored out and the problem reduced to one of two-dimensional wave diffraction by line segments. The two-dimensional problem of wave diffraction by thin impermeable structures has received considerable attention and references to this body of work can be found in the text by Linton and ∗Professor of Applied Mathematics, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, U.K.