Journal of Marine Science and Application

, Volume 16, Issue 4, pp 480–489 | Cite as

Wave analysis of porous geometry with linear resistance law

  • Jørgen Dokken
  • John Grue
  • Lars Petter Karstensen


The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.


wave analysis fish cages mean drift force wave exciting force added mass damping 


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The wave radiation-diffraction program WAMIT (version 5.3) was provided by Massachusetts Institute of Technology and Det Norske Veritas (now DNV-GL) through a mutual agreement with University of Oslo in 1994.


  1. An S, Faltinsen OM, 2012. Linear free-surface effects on a horizontally submerged and perforated 2D thin plate in finite and infinite water depths. Appl. Ocean Res., 37, 220–234. DOI: Scholar
  2. Behera H, Koley S, Sahoo T, 2015. Wave transmission by partial porous structures in two-layer fluid. Engng. An. with Bound. Elements, 58, 58–78. DOI: Scholar
  3. Chwang AT, 1983. A porous-wavemaker theory. J. Fluid Mech., 132, 395–406. DOI: Scholar
  4. Chwang AT, Chan AT, 1998. Interaction between porous media and wave motion. Annu. Rev. Fluid Mech., 30, 53–84. DOI: Scholar
  5. Chwang AT, Wu J, 1994. Wave scattering by submerged porous disk. J. Eng. Mech., 120, 2575–2587. DOI: (2575)CrossRefGoogle Scholar
  6. Faltinsen OM, 1990. Wave loads on offshore structures. Annu. Rev. Fluid Mech., 22, 35–56.CrossRefGoogle Scholar
  7. Finne S, Grue J, 1997. On the complete radiation-diffraction problem and wave-drift damping marine bodies in the yaw mode of motion. J. Fluid Mech., 357, 289–320. DOI: Scholar
  8. Grue J, Biberg D, 1993. Wave forces on marine structures with small speed in water of restricted depth. Appl. Ocean Res., 15, 121–135. DOI: Scholar
  9. Grue J, Palm E, 1993. The mean drift force and yaw moment on marine structures in waves and current. J. Fluid Mech., 250, 121–142. DOI: Scholar
  10. Grue J, Palm E, 1996. Wave drift damping of floating bodies in slow yaw-motion. J. Fluid Mech., 319, 323–352. DOI: Scholar
  11. Huang Z, Li Y, Liu Y, 2011. Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review. Ocean Engng., 38, 10311053. DOI: Scholar
  12. Jarlan GE, 1961. A perforated vertical wall break-water. Dock and Harb. Auth. XII, 486, 394–398.Google Scholar
  13. Koley S, Kaligatla RB, Sahoo T, 2015a. Oblique wave scattering by a vertical flexible porous plate. Stud. Appl. Math., 135, 134. DOI: 10.1111/sapm.12076MathSciNetCrossRefzbMATHGoogle Scholar
  14. Koley S, Behera H, Sahoo T, 2015b. Oblique wave trapping by porous structures near a wall. J. Engng. Mech., 141(3), 1–15. DOI: Scholar
  15. Laws EM, Livsey JL, 1978. Flow through screens. Annu. Rev. Fluid Mech., 10, 247–266.CrossRefGoogle Scholar
  16. Liu Y, Li HJ, 2013. Wave reflection and transmission by porous breakwaters: a new analytical solution. Coast. Engng., 78, 4652. DOI: Scholar
  17. Molin B, 1994. Second-order hydrodynamics applied to moored structures -A state-of-the-art survey. Ship Technology Res., 41, 59–84.Google Scholar
  18. Molin B, 2001. On the added mass and damping of periodic arrays or partially porous disks. J. Fluids and Struct., 15, 275–290. DOI: 10.1006/jfs.2000.0338CrossRefGoogle Scholar
  19. Molin B, 2011. Hydrodynamic modeling of perforated structures. Appl. Ocean Res., 33, 1–11. DOI: Scholar
  20. Molin B, Remy F, 2013. Experimental and numerical study of the sloshing motion in a rectangular tank with a perforated screen. J. Fluids and Struct., 43, 463–480. DOI: Scholar
  21. Newman JN, 1977. Marine hydrodynamics. MIT Press, 402.Google Scholar
  22. Newman JN, 2014. Cloaking a circular cylinder in water waves. Eur. J. Mech. B/Fluids, 47, 145–150. DOI: Scholar
  23. Nossen J, Grue J, Palm E, 1991. Wave forces on three-dimensional floating bodies with small forward speed. J. Fluid Mech., 227, 135–160. DOI: Scholar
  24. Taylor GI, 1956. Fluid flow in regions bounded by porous surfaces. Proc. Roy Soc. Lond. A, 234 (1199), 456–475. DOI: 10.1098/rspa.1956.0050CrossRefzbMATHGoogle Scholar
  25. Willams AN, Li W, Wang K-H, 2000. Water wave interaction with a floating porous cylinder. Ocean Engng., 27, 1–28. DOI: Scholar
  26. Yu X, 1995. Diffraction of water waves by porous breakwaters. J. Waterway, Port, Coastal, Ocean Engng., 121, 275282. DOI: Scholar
  27. Zhao F, Kinoshita T, Bao W, Wan R, Liang Z, Huang L, 2011a. Hydrodynamics identities and wave-drift force of a porous body. Appl. Ocean Res., 33, 169–177. DOI: Scholar
  28. Zhao F, Bao W, Kinoshita T, Itakura H, 2011b. Theoretical and experimental study of a porous cylinder floating in waves. J. Offsh. Mech. Arctc. Engng., 133/011301–1–10. DOI: 10.1115/1.4001435CrossRefGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jørgen Dokken
    • 1
  • John Grue
    • 1
  • Lars Petter Karstensen
    • 1
  1. 1.Mechanics Division, Department of MathematicsUniversity of OsloOsloNorway

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