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Approximate solution of the problem of scattering of surface water waves by a partially immersed rigid plane vertical barrier

Gayen, R and Gupta, Sourav and Chakrabarti, A (2016) Approximate solution of the problem of scattering of surface water waves by a partially immersed rigid plane vertical barrier. In: APPLIED MATHEMATICS LETTERS, 58 . pp. 19-25.

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Official URL: http://dx.doi.org/10.1016/j.aml.2016.01.018

Abstract

The problem of scattering of two dimensional surface water waves by a partially immersed rigid plane vertical barrier in deep water is re-examined. The associated mixed boundary value problem is shown to give rise to an integral equation of the first kind. Two direct approximate methods of solution are developed and utilized to determine approximate solutions of the integral equation involved. The all important physical quantity, called the Reflection Coefficient, is evaluated numerically, by the use of the approximate solution of the integral equation. The numerical results, obtained in the present work, are found to be in an excellent agreement with the known results, obtained earlier by Ursell (1947), by the use of the closed form analytical solution of the integral equation, giving rise to rather complicated expressions involving Bessel functions. (C) 2016 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords: First kind integral equation; Direct polynomial approximation; Chebyshev polynomials
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 15 Jun 2016 05:43
Last Modified: 15 Jun 2016 05:43
URI: http://eprints.iisc.ac.in/id/eprint/53941

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