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.
oblique wave scattering bottom undulation vertical barrier eigenfunction expansion Green’s integral theorem reflection and transmission coefficients
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A. Choudhary is grateful to the University Grants Commission (UGC), Government of India, for providing the research fellowship for pursuing Ph.D. degree at the Indian Institute of Technology Ropar, India. S. C. Martha is grateful to SERB-DST, Govt. of India for financial funding under grant number SB/FTP/MS-034/2013.
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