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 A. Choudhary,S. C. Martha.Scattering of Oblique Surface Water Waves by Thin Vertical Barrier Over Undulating Bed Topography[J].Journal of Marine Science and Application,2017,(2):190-198.[doi:10.1007/s11804-017-1411-0]
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Scattering of Oblique Surface Water Waves by Thin Vertical Barrier Over Undulating Bed Topography


Scattering of Oblique Surface Water Waves by Thin Vertical Barrier Over Undulating Bed Topography
A. Choudhary S. C. Martha
A. Choudhary S. C. Martha
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar-140001, India
oblique wave scatteringbottom undulationvertical barriereigenfunction expansionGreen’s integral theoremreflection and transmission coefficients
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 ofeigenfunction 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.


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Received date:2016-6-15;Accepted date:2016-12-31。
Foundation item:Supported by SERB-DST Grant (No. SB/FTP/MS-034/2013)
Corresponding author:S. C. Martha, Email: scmartha@gmail.com
Last Update: 2017-05-09