Journal of Engineering Mathematics

, Volume 19, Issue 4, pp 297–319 | Cite as

Diffraction of water waves by a moored, horizontal, flat plate

  • M. McIver


A Norwegian research group has investigated the feasibility of constructing a system of underwater structures which would act like a lens and focus water waves prior to harnessing their energy. In the present work we consider modelling one of these structures by a horizontal, flat plate which is moored to the seabed. The water is assumed to be incompressible and inviscid and two-dimensional, linear, irrotational theory is used. Solutions to the scattering and radiation potentials are obtained by the method of matched eigenfunction expansions. Comparisons are made with various approximate solutions and results are presented illustrating the effect of varying the mooring stiffness in the cables on both the responses of the plate and the far-field wave motion.


Radiation Mathematical Modeling Research Group Approximate Solution Industrial Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.E. Burke, Scattering of surface waves on an infinitely deep fluid, J. Mathematical Physics 5 (1964) 805–819.Google Scholar
  2. [2]
    W.R. Dean, On the reflection of surface waves by a submerged circular cylinder, Proc. Camb. Phil. Soc. 44 (1948) 483–491.Google Scholar
  3. [3]
    D.V. Evans, Power from water waves, Annual Review of Fluid Mechanics 13 (1981) 157–187.Google Scholar
  4. [4]
    D.V. Evans and P. McIver, Edge waves over a shelf: full linear theory, J. Fluid Mech. 142 (1984) 79–95.Google Scholar
  5. [5]
    T.R. Greene and A.E. Heins, Water waves over a channel of infinite depth, Quarterly J. of Applied Maths. 11 (1953) 201–214.Google Scholar
  6. [6]
    J. Grue and E. Palm, Reflection of surface waves by submerged cylinders, Applied Ocean Research 6 (1984) 54–60.Google Scholar
  7. [7]
    A.E. Heins, Water waves over a channel of finite depth with a submerged plane barrier, Canadian Journal of Maths. 2 (1950) 210–222.Google Scholar
  8. [8]
    E. Mchlum, A circular cylinder in water waves, Applied Ocean Research 2 (1980) 171–177.Google Scholar
  9. [9]
    E. Mchlum and J.J. Stamnes, On the fecusing of ocean swells and its significance in power production, Central Inst. for Indust. Res., Blindern, Oslo, SI Rep. 77 01 38 (1978).Google Scholar
  10. [10]
    C.C. Mel, The Applied Dynamics of Ocean Surface Waves, Wiley-Interscience, New York (1983).Google Scholar
  11. [11]
    C.C. Mel and J.L. Black, Scattering of surface waves by rectangular obstacles in water of finite depth, J. Fluid Mech. 38 (1960) 499–511.Google Scholar
  12. [12]
    J.N. Newman, Propagation of water waves past long two-dimensional obstacles, J. Fluid Mech. 23 (1965) 23–29.Google Scholar
  13. [13]
    M. Patarapanich, Maximum and zero reflection from a submerged plate. J. Waterway, Port, Coastal and Ocean Engineering 110 (1984) 171–181.Google Scholar
  14. [14]
    M. Patarapanich, Forces and moment on a horizontal plate due to wave scattering, Coastal Engineering 8 (1984) 279–301.Google Scholar
  15. [15]
    P.F. Siew and D.G. Hurley, Long surface waves incident on a submerged horizontal plate, J. Fluid Mech. 83 (1977) 141–151.Google Scholar
  16. [16]
    J.R. Thomas. The hydrodynamics of certain wave energy absorbers, Ph.D. Thesis, University of Bristol (1981).Google Scholar
  17. [17]
    F. Ursell, Surface waves on deep water in the presence of a submerged cylinder, Proc. Camb. Phil. Soc. 46 (1950) 141–158.Google Scholar
  18. [18]
    J.V. Wehausen and E.V. Laitone, Surface waves, Handbuch der Physik 9 (1960) 446–778.Google Scholar

Copyright information

© Martinus Nijhoff Publishers 1985

Authors and Affiliations

  • M. McIver
    • 1
  1. 1.School of MathematicsUniversity of BristolBristelUK

Personalised recommendations