Abstract:
The present study deals with the scattering of oblique
surface water waves by small undulation on the bottom in the
presence of a thin vertical barrier. Here, three different
configurations of vertical barriers are investigated. Perturbation
analysis is employed to determine the physical quantities, namely,
the reflection and transmission coefficients. In this analysis, many
different Boundary Value Problems (BVPs) are obtained out of
which the first two bvps are considered. The zeroth order bvp is
solved with the aid of eigenfunction expansion method. The first
order reflection and transmission coefficients are derived in terms
of the integrals by the method of the Green’s integral theorem. The
variation of these coefficients is plotted and analyzed for different
physical parameters. Furthermore, the energy balance relation, an
important relation in the study of water wave scattering, is derived
and checked for assuring the correctness of the numerical results
for the present problem.
