Water wave scattering by thick rectangular slotted barriers

This paper is concerned with scattering of surface water waves 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 barrier may be surface piercing and partially immersed, or bottom standing and submerged, or in the form of a submerged slotted thick block not extending down to the bottom, or in the form of a slotted thick wall extending from the free surface to the bottom. Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized in the mathematical analysis for solving first kind integral equations valid in the union of several disjoint intervals, to obtain very accurate numerical estimates for the reflection coefficient which is depicted graphically against the wave number in a number of figures for various configurations of the thick slotted barrier. Numerical codes prepared for this problem are valid for an arbitrary number of slots, the length of the slots as well as the wetted portions of the bar-tier for each configuration being unequal. However, to show the dependence of the reflection coefficient on the number of slots, results for a slotted wall with five slots are graphically displayed in one figure. Some results in the limiting cases have been compared with known results and good agreement is seen to have been achieved. New results are also presented showing total reflection at some moderate wave numbers for submerged slotted barriers. (C) 2002 Published by Elsevier Science Ltd.