Propagation of water waves over an asymmetrical rectangular trench

Assuming linear theory, the problem of water wave scattering by an asymmetric rectangular trench is investigated by employing Havelock’s expansion of water wave potential. A multi-term Galerkin approximation technique involving ultra-spherical Gegenbauer polynomials has been utilised for solving a first-kind vector integral equation, which is obtained in the analysis of the problem following Havelock’s inversion formulae. Numerical estimates for the reflection and transmission coefficients are depicted graphically for different configurations of the rectangular trench. Numerical results available in the literatures are recovered by using the present method and thereby confirming the correctness of the numerical results presented here.