Water wave scattering by thick rectangular slotted barriers in the presence of ice cover

This paper is concerned with the scattering of surface water waves by a thick vertical slotted barrier of rectangular cross-section with an arbitrary number of slots of unequal lengths present in water of finite depth with ice-covered surface. Two different geometrical configurations of the slotted barrier are considered, viz., (i) submerged and bottom standing and (ii) submerged slotted thick barrier. The problem is formulated in terms of an integral equation in disjoint intervals, by suitable matching of eigenfunction expansion of water wave potential. Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilised in the mathematical analysis for solving the integral equations to obtain very accurate numerical estimates for the reflection coefficient which is then depicted graphically against the wave number for various configurations of the thick slotted barrier. Also, for validation of mathematical results, the integral is solved using the boundary element method (BEM) in a very simple manner. The numerical comparison shows that BEM is a useful alternative method to solve such problems.