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Effect of Porous Uneven Seabed on a Water-Wave Diffraction Problem

  • Manas Ranjan Sarangi
  • Smrutiranjan Mohapatra
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Utilizing the linearized wave theory, the issue of the diffraction of obliquely progressive waves by a little contortion on a porous sea-bed is investigated. By the help of perturbation hypothesis, the related problem is diminished to a boundary value problem (BVP) for the first-order velocity potential function. Then the first-order potential function and, henceforth, the first-order reflection as well as transmission coefficients are evaluated by Fourier transform technique. A particular frame of sinusoidal ripples has been considered for verifying the theoretical results.

References

  1. 1.
    Chamberlain, P.G., Porter, D.: The modified mild-slope equations. J. Fluid Mech., 291, 393–407 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Davies, A.G.: The reflection of wave energy by undulations of the sea bed. Dyn. Atmos. Oceans, 6, 207–232 (1982).CrossRefGoogle Scholar
  3. 3.
    Davies A.G., Heathershaw A.D.: Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech., 144, 419–443 (1984)CrossRefGoogle Scholar
  4. 4.
    Kirby, J.T.: A general wave equation for waves over rippled beds. Journal of Fluid Mechanics, 162, 171–186 (1986)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Mei, C.C.: Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech., 152, 315–335 (1985)CrossRefGoogle Scholar
  6. 6.
    Mohapatra, S., Bora S.N.: Reflection and transmission of water waves in a two-layer fluid flowing through a channel with undulating bed. J. Appl. Math. Mech., 91, 46–56 (2011)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Mohapatra, S.: Scattering of oblique surface waves by the edge of small deformation on a porous ocean bed. J. Mar. Sci. Appl., 14, 156–162 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mohapatra, S.: The effect of surface-tension on scattering of water waves by small bottom undulation. ANZIAM J., 58(E), E39–E80 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mohapatra, S., Sarangi, M.R.: A note on the solution of water wave scattering problem involving small deformation on a porous channel-bed. J. Mar. Sci. Appl., 16, 10–19 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Manas Ranjan Sarangi
    • 1
  • Smrutiranjan Mohapatra
    • 1
  1. 1.VSS University of TechnologyBurlaIndia

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