Advertisement

Journal of Marine Science and Application

, Volume 16, Issue 4, pp 490–501 | Cite as

Oblique wave trapping by vertical permeable membrane barriers located near a wall

  • Santanu Koley
  • Trilochan Sahoo
Article

Abstract

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.

Keywords

surface waves flexible membrane porosity eigenfunction expansion least squares approximation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Behera H, Kaligatla R, Sahoo T, 2015a. Wave trapping by porous barrier in the presence of step type bottom. Wave Motion, 57, 219–230. DOI: 10.1016/j.wavemoti.2015.04.005MathSciNetCrossRefGoogle Scholar
  2. Behera H, Koley S, Sahoo T, 2015b. Wave transmission by partial porous structures in two-layer fluid. Engineering Analysis with Boundary Elements, 58, 58–78. DOI: 10.1016/j.enganabound.2015.03.010MathSciNetCrossRefGoogle Scholar
  3. Behera H, Mandal S, Sahoo T, 2013. Oblique wave trapping by porous and flexible structures in a two-layer fluid. Physics of Fluids, 25(11), 23–42. DOI: 10.1063/1.4832375CrossRefGoogle Scholar
  4. Cho I, Kee S, Kim M, 1997. The performance of flexiblemembrane wave barriers in oblique incident waves. Applied Ocean Research, 19(3), 171–182. DOI: 10.1016/S0141-1187(97)00017-5CrossRefGoogle Scholar
  5. Cho I, Kim M, 2000. Interactions of horizontal porous flexible membrane with waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(5), 245–253. DOI: 10.1061/(ASCE)0733-950X(2000)126:5(245)CrossRefGoogle Scholar
  6. Chwang AT, 1983. A porous-wavemaker theory. Journal of Fluid Mechanics, 132, 395–406. DOI: 10.1017/S0022112083001676CrossRefzbMATHGoogle Scholar
  7. Chwang A, Dong Z, 1984. Wave-trapping due to a porous plate. Proceedings of the 15th ONR Symposium on Naval Hydrodynamics, Washington, 407–414.Google Scholar
  8. Chwang AT, Li W, 1983. A piston-type porous wavemaker theory. Journal of Engineering Mathematics, 17(4), 301–313. DOI: 10.1007/BF00040174CrossRefzbMATHGoogle Scholar
  9. Dalrymple RA, Kirby JT, Seli, DJ, 1986. Wave trapping by breakwaters. Proceedings of the 20th Int. Conference on Coastal Engineering, Taipei, China, 1, 1820–1830.Google Scholar
  10. Hales LZ, 1981. Floating breakwaters: State of the art, literature review. Tech. report, USACE.Google Scholar
  11. Kaligatla R, Koley S, Sahoo T, 2015. Trapping of surface gravity waves by a vertical flexible porous plate near a wall. Zeitschrift fur angewandte Mathematik und Physik, 66(5), 2677–2702. DOI: 10.1007/s00033-015-0521-2MathSciNetCrossRefzbMATHGoogle Scholar
  12. Karmakar D, Bhattacharjee J, Soares CG, 2013. Scattering of gravity waves by multiple surface-piercing floating membrane. Applied Ocean Research, 39, 40–52. DOI: 10.1016/j.apor.2012.10.001CrossRefGoogle Scholar
  13. Kim M, Kee S, 1996. Flexible-membrane wave barrier. I: Analytic and numerical solutions. Journal of Waterway, Port, Coastal, and Ocean Engineering, 122(1), 46–53. DOI: 10.1061/(ASCE)0733-950X(1996)122:1(46)CrossRefGoogle Scholar
  14. Koley S, Behera H, Sahoo T, 2014. Oblique wave trapping by porous structures near a wall. Journal of Engineering Mechanics, 141(3), 04014122. DOI: 10.1061/(ASCE)EM.1943-7889.0000843CrossRefGoogle Scholar
  15. Koley S, Kaligatla R, Sahoo T, 2015a. Oblique wave scattering by a vertical flexible porous plate. Studies in Applied Mathematics, 135(1), 1–34. DOI: 10.1111/sapm.12076MathSciNetCrossRefzbMATHGoogle Scholar
  16. Koley S, Sahoo T, 2016. Oblique wave scattering by horizontal floating flexible porous membrane. Meccanica, 52, 125–138. DOI: 10.1007/s11012-016-0407-1MathSciNetCrossRefGoogle Scholar
  17. Koley S, Sahoo T, 2017a. Scattering of oblique waves by permeable vertical flexible membrane wave barriers. Applied Ocean Research, 62, 156–168. DOI: 10.1016/j.apor.2016.12.005CrossRefGoogle Scholar
  18. Koley S, Sahoo T, 2017b. Wave interaction with a submerged semicircular porous breakwater placed on a porous seabed. Engineering Analysis with Boundary Elements, 80, 18–37. DOI: 10.1016/j.enganabound.2017.02.019MathSciNetCrossRefGoogle Scholar
  19. Koley S, Sarkar A, Sahoo T, 2015b. Interaction of gravity waves with bottom-standing submerged structures having perforated outer-layer placed on a sloping bed. Applied Ocean Research, 52, 245–260. DOI: 10.1016/j.apor.2015.06.003CrossRefGoogle Scholar
  20. Kumar PS, Manam S, Sahoo T, 2007. Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid. Journal of Fluids and Structures, 23(4), 633–647. DOI: 10.1016/j.jfluidstructs.2006.10.011CrossRefGoogle Scholar
  21. Lamb H, 1945. Hydrodynamics. Dover Publications Inc., New York, 447.Google Scholar
  22. Leblond P, Mysak L, 1978. Waves in the ocean. Elsevier Publications, Amsterdam, 227.Google Scholar
  23. Lee WK, Lo EY, 2002. Surface-penetrating flexible membrane wave barriers of finite draft. Ocean Engineering 29(14), 1781–1804. DOI: 10.1016/S0029-8018(02)00007-0CrossRefGoogle Scholar
  24. Liu Y, Li HJ, 2012. Analysis of wave interaction with submerged perforated semi-circular breakwaters through multipole method. Applied Ocean Research, 34, 164–172. DOI: 10.1016/j.apor.2011.08.003CrossRefGoogle Scholar
  25. Meylan MH, Fitzgerald CJ, 2014. The singularity expansion method and near-trapping of linear water waves. Journal of Fluid Mechanics, 755, 230–250. DOI: 10.1017/jfm.2014.411MathSciNetCrossRefzbMATHGoogle Scholar
  26. Nazarov SA, Videman JH, 2011. Trapping of water waves by freely floating structures in a channel. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 467, 3613–3632. DOI: 10.1098/rspa.2011.0288MathSciNetCrossRefzbMATHGoogle Scholar
  27. Peregrine D, 2003. Water-wave impact on walls. Annual Review of Fluid Mechanics, 35(1), 23–43. DOI: 10.1146/annurev.fluid.35.101101.161153MathSciNetCrossRefzbMATHGoogle Scholar
  28. Sahoo T, Lee M, Chwang A, 2000. Trapping and generation of waves by vertical porous structures. Journal of Engineering Mechanics, 126(10), 1074–1082. DOI: 10.1061/(ASCE)0733-9399(2000)CrossRefGoogle Scholar
  29. Wang KH, Ren X, 1994. An effective wave-trapping system. Ocean Engineering, 21(2), 155–178. DOI: 10.1016/0029-8018(94)90036-1CrossRefGoogle Scholar
  30. Williams A, Wang K, 2003. Flexible porous wave barrier for enhanced wetlands habitat restoration. Journal of Engineering Mechanics, 129(1), 1–8. DOI: 10.1061/(ASCE)0733-9399(2003)129:1(1)CrossRefGoogle Scholar
  31. Yip T, Sahoo T, Chwang AT, 2002. Trapping of surface waves by porous and flexible structures. Wave Motion, 35(1), 41–54. DOI: 10.1016/S0165-2125(01)00074-9CrossRefzbMATHGoogle Scholar
  32. Yu X, 1995. Diffraction of water waves by porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 121(6), 275–282. DOI: 10.1061/(ASCE)0733-950X(1995)121:6(275)CrossRefGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia
  2. 2.Department of Ocean Engineering and Naval ArchitectureIndian Institute of TechnologyKharagpurIndia

Personalised recommendations