Journal of Engineering Mathematics

, Volume 52, Issue 4, pp 355–377 | Cite as

Waves Past Porous Structures in a Two-layer Fluid

  • S. R. Manam
  • T. Sahoo


Havelock’s type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.


porous barriers reflection coefficient source potentials surface and interfacial waves wave trapping 


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  1. 1.
    Havelock, T.H. 1929Forced surface wave on waterPhil. Mag.8569576Google Scholar
  2. 2.
    Linton, C.M., McIver, M. 1995The interaction of waves with horizontal cylinders in two-layer fluidsJ. Fluid Mech.304213229Google Scholar
  3. 3.
    Motygin, O.V., Kuznetsov, N.G. 1997The wave resistance of a two-dimensional body moving forward in a two-layer fluidJ. Engng. Math.355372CrossRefGoogle Scholar
  4. 4.
    Kundu, P.K., Cohen, I.M. 2002Fluid MechanicsAcademic PressNew York730Google Scholar
  5. 5.
    R.W. Yeung and T. Nguyen, Radiation and diffraction of waves in a two-layer fluid. Proc. 22nd Symposium on Naval Hydrodynamics Washington, DC: National Academy Press (1999) pp. 875–891.Google Scholar
  6. 6.
    Cadby, J.R., Linton, C. M. 2000Three dimensional water wave scattering in two-layer fluidsJ. Fluid Mech.423155173CrossRefGoogle Scholar
  7. 7.
    Zilman, G., Miloh, T. 1995Hydrodynamics of a body moving over a mud layer-Part I:, Wave resistanceJ. Ship Res.39194201Google Scholar
  8. 8.
    Zilman, G., Kagan, L., Miloh, T. 1996Hydrodynamics of a body moving over a mud layer-Part II: Added-mass and damping coefficientsJ. Ship Res.403945Google Scholar
  9. 9.
    Barthelemy, E., Kabbaj, A., Germain, J.P. 2000Long surface wave scattered by a step in a two-layer fluidFluid Dynam. Res.26235255CrossRefGoogle Scholar
  10. 10.
    Linton, C.M., Cadby, J.R. 2002Scattering of oblique waves in a two-layer fluidJ. Fluid Mech.461343364CrossRefGoogle Scholar
  11. 11.
    Mandal, B.N., Chakrabarti, A. 2003A generalization to the hybrid Fourier transform and its applicationAppl. Math. Lett.16703708CrossRefGoogle Scholar
  12. 12.
    Chwang, A.T. 1983A porous wavemaker theoryJ. Fluid Mech.132395406Google Scholar
  13. 13.
    Chwang, A.T., Li, W. 1983A piston-type porous wavemaker theoryJ. Engng. Math.17301313Google Scholar
  14. 14.
    Lee, M.M., Chwang, A.T. 2000Scattering and radiation of water waves by permeable barriersPhys. Fluids125465CrossRefGoogle Scholar
  15. 15.
    Sherief, H.H., Faltas, M.S., Saad, E.I. 2003Forced gravity waves in two-layered fluids with the upper fluid having a free surfaceCan. J. Phys.81675689CrossRefGoogle Scholar
  16. 16.
    Sahoo, T. 1998On the generation of water waves by cylindrical porous wavemakerActa Mech.126231239CrossRefGoogle Scholar
  17. 17.
    J.V. Wehausen and E.V. Laitone, Surface waves. In: S. Flugge (ed.), Handbuck der Physik, vol. 9, Springer Verlag (1960) pp. 446–778.Google Scholar
  18. 18.
    Yu, X., Chwang, A.T. 1994Wave induced oscillation in harbour with porous breakwatersJ. Waterway, Port, Coast. and Ocean Engrg.120125144Google Scholar
  19. 19.
    Sollitt, C.K., Cross, R.H. 1972Wave transmission through permeable breakwatersCanadaVancouver182746Proc. 13th ASCE Conf. Coastal Eng.Google Scholar
  20. 20.
    Chwang, A.T., Chan, A.T. 1998Interaction between porous media and wave motionAnn. Rev. Fluid Mech.305384CrossRefGoogle Scholar
  21. 21.
    Sahoo, T., Lee, M.M., Chwang, A.T. 2000Trapping and generation of waves by vertical porous structureJ. Engng. Mech.12610741082CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Ocean Engineering and Naval ArchitectureIITKharagpurIndia
  2. 2.CMLA, ENS de CachanCedexFrance

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