Waterwave scattering by two submerged plane vertical barriers—Abel integralequation approach
 Soumen De,
 B. N. Mandal,
 A. Chakrabarti
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Abstract
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.
 Ursell F (1947) The effect of a fixed vertical barrier on surface waves in deep water. Proc Camb Phil Soc 43: 374–382 CrossRef
 Evans DV (1970) Diffraction of water waves by a submerged vertical plate. J Fluid Mech 40: 433–451 CrossRef
 Porter D (1972) The transmission of surface waves through a gap in a vertical barrier. Proc Camb Phil Soc 71: 411–421 CrossRef
 Kuznetsov N, McIver P, Linton CM (2001) On uniqueness and trapped modes in the water wave problem for vertical barriers. Wave Motion 33: 283–307 CrossRef
 Williams WE (1966) Note on the scattering of water waves by a vertical barrier. Proc Camb Phil Soc 62: 507–509 CrossRef
 Levine H, Rodemich F (1958) Scattering of surface waves on an ideal fluid. Stanford University Technical Report Number 78, Math Stat Lab
 Jarvis RJ (1971) The scattering of surface waves by two vertical plane barriers. J Inst Maths Appl 7: 207–215
 Evans DV, Morris CAN (1972) Complementary approximations to the solution of a problem in water waves. J Inst Maths Appl 10: 1–9 CrossRef
 Newman JN (1974) Interaction of water waves with two closely spaced vertical obstacles. J Fluid Mech 66: 97–106 CrossRef
 McIver P (1985) Scattering of water waves by two surfacepiercing vertical barriers. IMA J Appl Math 35: 339–355 CrossRef
 Mandal BN, Dolai DP (1994) Oblique water wave diffraction by thin vertical barriers in water of uniform finite depth. Appl Ocean Res 16: 195–203 CrossRef
 Das P, Dolai DP, Mandal BN (1997) Oblique water wave diffraction by two parallel thin barriers with gaps. J Waterw Port Coast Ocean Eng 123: 163–171 CrossRef
 Porter R, Evans DV (1995) Complementary approximations to waves scattering by vertical barriers. J Fluid Mech 294: 155–180 CrossRef
 Dean WR (1945) On the reflection of surface waves by submerged plane barrier. Proc Camb Phil Soc 4: 231–238 CrossRef
 Faulkner TR (1966) The diffraction of any obliquely incident surface wave by a vertical barrier of finite depth. Proc Camb Phil Soc 62: 829–838 CrossRef
 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
 20090901
 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