Journal of Engineering Mathematics

, Volume 76, Issue 1, pp 33–57 | Cite as

The effect of slatted screens on waves

  • S. CrowleyEmail author
  • R. Porter


A linearised model is proposed for the transmission of waves through thin vertical porous barriers, where both the inertial and dominant quadratic drag effects are included. A boundary-value problem is developed in which linear boundary conditions holding along the length of the screen are derived from a pair of canonical wave problems, one including an exact geometric description of a slatted screen to determine an inertia coefficient and the other using a quadratic drag law to determine an equivalent linear drag coefficient. The model is then applied to a range of wave scattering and sloshing problems involving thin vertical slatted screens in various settings. In each case results are verified by comparison to the solution of a direct non-linear calculation where the effects of drag have been isolated. We show that the solution to our canonical problem provides a good approximation to the solution of each of the model problems.


Inertial effects Quadratic drag law Slatted screens Water waves 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baines WD, Peterson EG (1951) An investigation of flow through screens. Trans ASME 73: 467–479Google Scholar
  2. 2.
    Bennett GS, McIver P, Smallman JV (1992) A mathematical model of a slotted wavescreen breakwater. Coast Eng 18: 231–249CrossRefGoogle Scholar
  3. 3.
    Dalrymple RA, Losada MA, Martin PA (1991) Reflection and transmission from porous structures under oblique wave attack. J Fluid Mech 224: 624–644ADSCrossRefGoogle Scholar
  4. 4.
    Evans DV (1976) A theory for wave-power absorption by oscillating bodies. J Fluid Mech 77(1): 1–25ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Evans DV (1990) The use of porous screens as wave dampers in narrow wave tanks. J Eng Math 24(3): 203–212CrossRefGoogle Scholar
  6. 6.
    Faltinsen OM, Timokha AN (2011) Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen. J Sound Vib 330: 1490–1503ADSCrossRefGoogle Scholar
  7. 7.
    Faltinsen OM, Firoozkoohi R, Timokha AN (2010) Analytical modeling of liquid sloshing in a two-dimensional rectangular tank with a slat screen. J Eng Math 70: 93–109MathSciNetCrossRefGoogle Scholar
  8. 8.
    Faltinsen OM, Firoozkoohi R, Timokha AN (2011) Steady-state liquid sloshing in a rectangular tank with a slat-type screen in the middle: Quasilinear modal analysis and experiments. Phys Fluids 23(4), Art. No. 042101Google Scholar
  9. 9.
    Isaacson M, Premasiri S, Yang G (1998) Wave interactions with vertical slotted barrier. J Waterw Port Coast Ocean Eng 124(3): 118–126CrossRefGoogle Scholar
  10. 10.
    Kondo H, Toma, S (1972) Reflection and transmission for a porous structure. In: Proceedings of 13th Coastal Engineering Conference, Vancouver 1847–1866Google Scholar
  11. 11.
    Madsen OS (1974) Wave transmission through porous structures. J Waterw Harb Coast Eng Div 100(3): 169–188Google Scholar
  12. 12.
    McIver P (1999) Water-wave diffraction by thin porous breakwater. J Waterw Port Coast Ocean Eng 125: 66–70CrossRefGoogle Scholar
  13. 13.
    McIver P (2005) Diffraction of water waves by a segmented permeable breakwater. J Waterw Port Coast Ocean Eng 131: 69–76CrossRefGoogle Scholar
  14. 14.
    Mei CC (1976) Power extraction from water waves. J Ship Res 20: 63–66Google Scholar
  15. 15.
    Mei CC (1983) The applied dynamics of ocean surface waves. World ScientificGoogle Scholar
  16. 16.
    Newman JN (1976) The interaction of stationary vessels with regular waves. In: Proceedings of 11th Symposium on Naval Hydrodynamics, London, pp 491–501Google Scholar
  17. 17.
    Porter R, Evans DV (1995) Complementary approximations to wave scattering by vertical barriers. J Fluid Mech 294: 155–180MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    Sollitt CK, Cross RH (1972) Wave transmission through permeable breakwaters. In: Proceedings of 13th Coastal Engineering Conference, Vancouver, pp 1827–1846Google Scholar
  19. 19.
    Sulisz W (1985) Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. J Coast Eng 9(4): 371–386CrossRefGoogle Scholar
  20. 20.
    Tait MJ (2008) Modelling and preliminary design of a structure-TLD system. Eng Struct 30(10): 2644–2655CrossRefGoogle Scholar
  21. 21.
    Tait MJ, El Damatty AA, Isyumov N, Siddique MR (2005) Numerical flow models to simulate tuned liquid dampers (TLD) with slat screens. J Fluids Struct 20: 1007–1023CrossRefGoogle Scholar
  22. 22.
    Tuck EO (1975) Matching problems involving flow through small holes. Adv Appl Mech 15: 89–158MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wu J, Wan Z, Fang Y (1998) Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Eng 25(9): 767–779CrossRefGoogle Scholar
  24. 24.
    Yu X (1995) Diffraction of water waves by porous breakwaters. J Waterw Port Coast Ocean Eng 121: 275–282CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK

Personalised recommendations