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Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

De, Soumen and Mandal, BN and Chakrabarti, A (2009) Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach. In: Journal of Engineering Mathematics, 65 (1). pp. 75-87.

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The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Keywords: Abel integral equations;Reflection and transmission coefficients;Two barriers;Wave scattering.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 21 Dec 2009 11:59
Last Modified: 19 Sep 2010 05:42
URI: http://eprints.iisc.ac.in/id/eprint/22631

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