Water wave scattering by pair of porous barriers in the presence of a bottom-standing rectangular obstacle

Oblique wave scattering by a pair of partially immersed porous barriers, placed (i) on one side of (Position I), (ii) just above (Position II) and (iii) on the two sides (Position III) of a thick rectangular bottom-standing rigid obstacle, is studied here. The mathematical formulation and solution procedure of the corresponding boundary value problem are discussed using Havelock's expansion and Galerkin's approximation technique. During the solution procedure, a set of first-kind Fredholm-type integral equations is solved approximately by choosing suitable basis functions (Chebyshev and Gegenbauer polynomials). To address the singularities of order half and one-third that appear at the submerged edges of the thin barriers and the corners of the thick obstacle, appropriate basis polynomials with suitable weight functions are chosen in Galerkin's approximation. The reflection and transmission coefficients, dissipating wave energy, and dimensionless wave force are computed for various values of different parameters and depicted graphically in quite a number of figures. The numerical results for some special cases are compared with those available in the literature and excellent agreement has seen to have been achieved thus validating the correctness of the numerical method presented here. Based on numerical results it is observed that Position III of the barriers is more effective than Position I and Position II in resisting wave loads on marine areas and attenuating wave energy.