Journal of Engineering Mathematics

, Volume 65, Issue 1, pp 75–87

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


  • Soumen De
    • Physics and Applied Mathematics UnitIndian Statistical Institute
    • Physics and Applied Mathematics UnitIndian Statistical Institute
  • A. Chakrabarti
    • Department of MathematicsIndian Institute of Science

DOI: 10.1007/s10665-009-9265-3

Cite this article as:
De, S., Mandal, B.N. & Chakrabarti, A. J Eng Math (2009) 65: 75. doi:10.1007/s10665-009-9265-3


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.


Abel integral equationsReflection and transmission coefficientsTwo barriersWave scattering
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© Springer Science+Business Media B.V. 2009