Oblique water wave scattering by two unequal vertical barriers

Scattering of an obliquely incident wave train by two non-identical thin vertical barriers either partially immersed or fully submerged in infinitely deep water was studied by employing Havelock’s expansion of water wave potential and reducing the problem ultimately to the solution of a pair of vector integral equations of the first kind. A one-term Galerkin approximation in terms of a known exact solution of the integral equation corresponding to a single vertical barrier is used to obtain very accurate numerical estimates for the reflection and transmission coefficients. The reflection coefficient is depicted graphically for two different arrangements of the vertical barriers. It is observed that total reflection is possible for some discrete values of the wavenumber only when the barriers are identical, either partially immersed or completely submerged. As the separation length between the two vertical barriers increases, the reflection coefficient becomes oscillatory as a function of the wavenumber, which is due to multiple reflections by the barriers. Also, as the separation length becomes very small, the known results for a single barrier are obtained for normal incidence of the wave train.