Water wave scattering by three thin vertical barriers arranged asymmetrically in deep water

Abstract

The paper involves oblique scattering of water waves by three non-identical thin vertical barriers arranged asymmetrically in deep water. The asymmetry in the configuration of the barriers is in the sense that the outer barriers are situated at two different distances from the inner (middle) barrier. Two geometries of the barriers have been considered. In the first one, the two outer barriers are partially immersed and the inner barrier is completely submerged and extends infinitely downwards while the second one is its complementary. Each problem is reduced to a system of three simultaneous first kind integral equations involving differences of potential functions across the barriers. These integral equations are solved approximately by employing single-term Galerkin’s approximations where the single term is the exact solution of the corresponding integral equation arising in the problem of scattering of normally incident water waves by a single thin vertical barrier in deep water. Fairly accurate numerical estimates for the reflection and transmission coefficients are obtained which satisfy the energy identity. For both the configurations of the barriers, the behavior of reflection coefficient is observed by depicting it graphically against wavenumber for different values of various parameters. It is observed that the reflection coefficient vanishes for a sequence of discrete wavenumbers only when the outer two barriers are identical and equidistant from the inner barrier. However, this phenomenon may differ sometimes for the second configuration of the barriers. Numerical results available in the literature are recovered as special cases thereby validating the accuracy of the numerical estimates obtained here.