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Use of Abel integral equations in water wave scattering by two surface-piercing barriers

De, Soumen and Mandal, BN and Chakrabarti, A (2010) Use of Abel integral equations in water wave scattering by two surface-piercing barriers. In: Wave Motion, 47 (5). pp. 279-288.

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Official URL: http://dx.doi.org/10.1016/j.wavemoti.2009.12.002


In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Publication: Wave Motion
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Water wave scattering;Plane vertical barriers;Abel integral equations;Reflection and transmission coefficients
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 25 Jun 2010 04:21
Last Modified: 19 Sep 2010 06:08
URI: http://eprints.iisc.ac.in/id/eprint/28281

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