Wave Transformation Due to a Submerged Porous Block Associated with a Vertical Barrier

  • K. R. Athul Krishna
  • V. Venkateswarlu
  • D. KarmakarEmail author
Conference paper


In the present study, the combination of vertical porous barrier along with the porous block is proposed for wave energy damping. Three types of vertical barriers such as (a) fully extended barrier (b) bottom-standing barrier and (c) surface piercing barrier away from the porous structure are analysed for wave trapping. The finite spacing in between vertical barrier and the porous structure is proposed for better wave trapping. The continuity of velocity and pressure at the interfaces of vertical barrier and porous structure are considered and the eigenfunction expansion method is adopted to determine the wave transformation characteristics due to the presence of submerged vertical barrier and porous block. The resistance and reactance offered by the porous structure are taken into account using the complex dispersion relation proposed by Sollitt and Cross (1972). The effect of structural porosity, width of the structure and angle of incidence on wave transformation due to the vertical barrier away from the porous structure are examined in detail. The results are compared and validated with the available literature for specific configurations as in Sollitt and Cross (1972) and Mallayachari and Sundar (1994). The study suggests that the increase in the structural porosity enhances the wave energy damping and global minima is achieved in the wave reflection coefficient due to the formation of standing waves by the breakwater system. The proposed structure can be adopted in leeward, port and harbour regions to achieve the tranquillity condition.


Eigenfunction expansion method Wave reflection coefficient Wave transmission coefficient Porosity Friction factor 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors are thankful to NITK Surathkal and Ministry of Human Resource Development (MHRD), Government of India, New Delhi for providing financial and necessary support to perform the research work.


  1. [1].
    Abul-Azm, A.G., (1994). Wave diffraction by double flexible breakwaters. Applied Ocean Research, 16(2), 87-99.CrossRefGoogle Scholar
  2. [2].
    Appiott, J., Dhanju, A. and Sain, C.B., (2014). Encouraging renewable energy in the offshore environment. Ocean & Coastal Management, 90, 58- 64.Google Scholar
  3. [3].
    Behera, H. and Ng, C.O., (2018). Interaction between oblique waves and multiple bottom-standing flexible porous barriers near a rigid wall. Meccanica, 53(4-5), pp.871-885.CrossRefGoogle Scholar
  4. [4].
    Burke, J.E., (1964). Scattering of surface waves on an infinitely deep fluid. Journal of Mathematical Physics, 5(6), 805-819.CrossRefGoogle Scholar
  5. [5].
    Chwang, A. T. (1983). A porous-wavemaker theory. Journal of Fluid Mechanics, 132, 395-406.CrossRefGoogle Scholar
  6. [6].
    Dalrymple, R. A., Losada, M. A., and Martin, P. A. (1991). Reflection and transmission from porous structures under oblique wave attack. Journal of Fluid Mechanics, 224, 625-644.CrossRefGoogle Scholar
  7. [7].
    Dattatri, J., Raman, H. and Shankar, N.J., (1978). Performance characteristics of submerged breakwaters. Coastal Engineering Proceedings, 1(16).Google Scholar
  8. [8].
    Fugazza, M. and Natale, L., (1992). Hydraulic design of perforated breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 118(1), 1-14.CrossRefGoogle Scholar
  9. [9].
    Gu, G.Z. and Wang, H., (1992). Numerical modeling for wave energy dissipation within porous submerged breakwaters of irregular cross section. Coastal Engineering Proceedings, 1(23).Google Scholar
  10. [10].
    Isaacson, M., Baldwin, J., Premasiri, S., & Yang, G. (1999). Wave interactions with double slotted barriers. Applied Ocean Research, 21(2), 81-91.Google Scholar
  11. [11].
    Kaligatla, R. B., Tabssum, S., and Sahoo, T. (2018). Effect of bottom topography on wave scattering by multiple porous barriers. Meccanica, 53(4-5), 887-903.CrossRefGoogle Scholar
  12. [12].
    Karmakar, D. and Guedes Soares, C., (2012). Oblique scattering of gravity waves by moored floating membrane with changes in bottom topography. Ocean Engineering, 54, pp.87-100.CrossRefGoogle Scholar
  13. [13].
    Karmakar, D. and Guedes Soares, C., (2014). Wave transformation due to multiple bottom-standing porous barriers. Ocean Engineering, 80, pp.50-63.CrossRefGoogle Scholar
  14. [14].
    Karmakar, D. and Guedes Soares, C., (2015). Propagation of gravity waves past multiple bottom-standing barriers. Journal of Offshore Mechanics and Arctic Engineering, 137, 011101, 1-10.Google Scholar
  15. [15].
    Koley, S. and Sahoo, T., (2017). Oblique wave trapping by vertical permeable membrane barriers located near a wall. Journal of Marine Science and Application, 16(4), 490-501.CrossRefGoogle Scholar
  16. [16].
    Koley, S. and Sahoo, T., 2017. Scattering of oblique waves by permeable vertical flexible membrane wave barriers. Applied Ocean Research, 62, pp.156-168.CrossRefGoogle Scholar
  17. [17].
    Liu, Y., Li, H.J. and Li, Y.C., 2012. A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness. Ocean Engineering, 42, pp.83-92.CrossRefGoogle Scholar
  18. [18].
    Losada, I.J., Losada, M.A. and Baquerizo, A., (1993). An analytical method to evaluate the efficiency of porous screens as wave dampers. Applied Ocean Research, 15(4), 207-215.CrossRefGoogle Scholar
  19. [19].
    Losada, I.J., Losada, M.A. and Roldán, A.J., (1992). Propagation of oblique incident waves past rigid vertical thin barriers. Applied Ocean Research, 14(3), 191-199.CrossRefGoogle Scholar
  20. [20].
    Madsen, P. A. (1983). Wave reflection from a vertical permeable wave absorber. Coastal Engineering, 7(4), 381-396.CrossRefGoogle Scholar
  21. [21].
    Mallayachari, V., and Sundar, V. (1994). Reflection characteristics of permeable seawalls. Coastal Engineering, 23(1-2), 135-150.CrossRefGoogle Scholar
  22. [22].
    Mani, J.S., (2009). Experimental and numerical investigations on zigzag porous screen breakwater. Natural Hazards, 49(2), 401-409.CrossRefGoogle Scholar
  23. [23].
    Mendez, F. J., & Losada, I. J. (2004). A perturbation method to solve dispersion equations for water waves over dissipative media. Coastal engineering, 51(1), 81-89.Google Scholar
  24. [24].
    Sahoo, T., Lee, M.M. and Chwang, A.T., (2000). Trapping and generation of waves by vertical porous structures. Journal of Engineering Mechanics, 126(10), 1074-1082.CrossRefGoogle Scholar
  25. [25].
    Sollitt, C.K. and Cross, R.H., (1972). Wave transmission through permeable breakwaters. In Coastal Engineering, 1827-1846.Google Scholar
  26. [26].
    Sulisz, W., (1985). Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coastal Engineering, 9(4), 371-386.CrossRefGoogle Scholar
  27. [27].
    Yu, X. and Chwang, A.T., (1993). Analysis of wave scattering by submerged circular disk. Journal of Engineering Mechanics, 119(9), pp.1804-1817.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • K. R. Athul Krishna
    • 1
  • V. Venkateswarlu
    • 1
  • D. Karmakar
    • 1
    Email author
  1. 1.Department of Applied Mechanics and HydraulicsNational Institute of Technology KarnatakaSurathkalIndia

Personalised recommendations