Journal of Engineering Mathematics
, Volume 65, Issue 1, pp 7587
First online:
Waterwave scattering by two submerged plane vertical barriers—Abel integralequation approach
 Soumen DeAffiliated withPhysics and Applied Mathematics Unit, Indian Statistical Institute
 , B. N. MandalAffiliated withPhysics and Applied Mathematics Unit, Indian Statistical Institute Email author
 , A. ChakrabartiAffiliated withDepartment of Mathematics, Indian Institute of Science
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The classical problem of surface waterwave 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 complexvariable theory to solve the problem.
Keywords
Abel integral equations Reflection and transmission coefficients Two barriers Wave scattering Title
 Waterwave scattering by two submerged plane vertical barriers—Abel integralequation approach
 Journal

Journal of Engineering Mathematics
Volume 65, Issue 1 , pp 7587
 Cover Date
 200909
 DOI
 10.1007/s1066500992653
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Abel integral equations
 Reflection and transmission coefficients
 Two barriers
 Wave scattering
 Industry Sectors
 Authors

 Soumen De ^{(1)}
 B. N. Mandal ^{(1)}
 A. Chakrabarti ^{(2)}
 Author Affiliations

 1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700108, India
 2. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India