Reflection by Slotted Thick Barriers under Oblique Wave Attack: A Numerical Study

Abstract

Abstract

This paper is concerned with scattering of an obliquely incident surface water wave by a thick vertical slotted barrier of rectangular cross section with an arbitrary number of slots of unequal lengths along the vertical direction, and present in finite depth water. Four different geometrical configurations of the slotted barrier are considered. The problem is reduced to solving first kind integral equations valid in the union of several disjoint intervals. Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to solve these integral equations to obtain very accurate numerical estimates for the reflection coefficient, which are depicted graphically against the wave number for each configuration of the slotted barrier. Numerical codes prepared for this problem are valid for an arbitrary number of slots, the lengths of the slots as well as the wetted portions of the barrier for each configuration being unequal. Some results in the limiting cases have been compared with known results and good agreement is seen to have been achieved.