Wave diffraction through a perforated breakwater

Abstract

Linear theory is used to examine the diffraction of surface water waves through an arbitrary arrangement of gaps in an infinite, straight breakwater standing in water of uniform quiescent depth. The governing boundary-value problem is reduced to an integral equation posed on the union of the gaps, for which a number of embedding formulae are derived. These formulae allow the solution of the diffraction problem for any incident wave angle to be expressed explicitly in terms of its solutions for 2N distinct incident angles, for example, where N is the number of gaps. If the breakwater arrangement is symmetric, solutions for only N distinct incident angles are required to generate the solution for any other angle. Numerical solutions of the integral equation, obtained by a variational method, confirm that computational saving obtained by the embedding approach is considerable. The techniques described may be applied to a range of similar problems.