Skip to main content
SpringerLink
Log in

Analytical study for oblique wave interaction with a submerged horizontal perforated plate near a partially reflecting vertical wall

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

A novel iterative analytical solution is developed to study the oblique wave interaction with a horizontally submerged perforated plate near a partially reflecting vertical wall. The boundary condition on the perforated plate is considered as a quadratic pressure drop to incorporate the effect of wave height on the wave energy dissipation. The boundary value problem is analyzed analytically under the assumptions of small amplitude wave theory. To validate the analytical model, an iterative solution based on MBEM (multi-domain boundary element method) is independently developed, and the comparison between the analytical solution and the experimental data are given. The performance characteristics of a submerged perforated plate before a partially reflecting vertical wall is studied by analyzing the hydrodynamic coefficients of the system for the effects of plate porosity, relative plate width, spacing, depth of submergence, and the direction of wave attack. The proposed model is expected to act as an effective breakwater in the attenuation of wave energy for the creation of a tranquillity zone in the marine environment. Moreover, the analytical model developed in the present study can be effective and reliable for practical preliminary design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

\(h\) :

Water depth

\(h_{1}\) :

Depth of submergence of perforated plate

\(h_{2}\) :

Space between the plate and the seabed

B :

Horizontal projected length of the plate

D :

Space between the perforated plate and the vertical wall

H :

Incident wave height

\(\omega\) :

Incident wave frequency

\(k_{0}\) :

Incident wave number

\(K_{R}\) :

Reflection coefficient

\(C_{R}\) :

Reflection coefficient of the vertical wall

\(\mu\) :

Plate porosity

\(\alpha\) :

Discharge coefficient

C :

Blockage coefficient

b :

Plate thickness

\(G\) :

Greens function

\({{\partial G} \mathord{\left/ {\vphantom {{\partial G} {\partial n}}} \right. \kern-\nulldelimiterspace} {\partial n}}\) :

Directional derivative of greens function

\(\Gamma\) :

Boundary of the computation domain

\(r\) :

Distance between source and field point

\(\lambda\) :

Wavelength

References

  1. Franco L (1994) Vertical breakwaters: the Italian experience. Coast Eng 22(1–2):31–55

    Article  Google Scholar 

  2. Oumeraci H (1994) Review and analysis of vertical breakwater failures—lessons learned. Coast Eng 22(1–2):3–29

    Article  Google Scholar 

  3. Cuomo G, Allsop W, Bruce T, Pearson J (2010) Breaking wave loads at vertical seawalls and breakwaters. Coast Eng 57(4):424–439

    Article  Google Scholar 

  4. Christie, S., Dong, J. S., and Charles, L. (2001). Ocean Waves Propagating over a Submerged Breakwater in Front of a Vertical Wall. Coasts & Ports 2001, In: Proceedings of the 15th Australasian Coastal and Ocean Engineering Conference, the 8th Australasian Port and Harbour Conference. Barton, A.C.T.: Institution of Engineers, Australia: pp 539–544

  5. Jeng DS, Schacht C, Lemckert C (2005) Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall. Ocean Eng 32(17–18):2231–2240

    Article  Google Scholar 

  6. Munireddy MG, Neelamani S (2004) Wave pressure reduction on vertical seawalls/Caisson due to an offshore breakwater. Indian J Mar Sci 33(4):329–337

    Google Scholar 

  7. Muni-Reddy MG, Neelamani S (2006) Wave interaction with caisson defenced by an offshore low-crested breakwater. J Coast Res 3:1767–1770

    Google Scholar 

  8. Koraim AS, Heikal EM, Zaid AA (2014) Hydrodynamic characteristics of porous seawall protected by submerged breakwater. Appl Ocean Res 46:1–14

    Article  Google Scholar 

  9. Koley S, Sahoo T (2017) Oblique wave trapping by vertical permeable membrane barriers located near a wall. J Mar Sci Appl 16(4):490–501

    Article  Google Scholar 

  10. Zhao Y, Li HJ, Liu Y (2017) Oblique wave scattering by a submerged porous breakwater with a partially reflecting sidewall. J Mar Sci Technol 25(4):383–392

    Google Scholar 

  11. Yu X, Chwang AT (1994) Water waves above submerged porous plate. J Eng Mech 120(6):1270–1282

    Google Scholar 

  12. Yu X (2002) Functional performance of a submerged and essentially horizontal plate for offshore wave control: a review. Coast Eng J 44(02):127–147

    Article  Google Scholar 

  13. Neves MDG, Losada IJ, Losada MA (2000) Short-wave and wave group scattering by submerged porous plate. J Eng Mech 126(10):1048–1056

    Google Scholar 

  14. Neelamani S, Reddy MS (1992) Wave transmission and reflection characteristics of a rigid surface and submerged horizontal plate. Ocean Eng 19(4):327–341

    Article  Google Scholar 

  15. Liu Y, Li HJ, Li YC (2012) A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness. Ocean Eng 42:83–92

    Article  Google Scholar 

  16. Neelamani S, Gayathri T (2006) Wave interaction with twin plate wave barrier. Ocean Eng 33(3–4):495–516

    Article  Google Scholar 

  17. Liu Y, Li YC (2011) An alternative analytical solution for water-wave motion over a submerged horizontal porous plate. J Eng Math 69(4):385–400

    Article  MathSciNet  MATH  Google Scholar 

  18. Cho IH, Koh HJ, Kim JR, Kim MH (2013) Wave scattering by dual submerged horizontal porous plates. Ocean Eng 73:149–158

    Article  Google Scholar 

  19. Cho IH, Kim MH (2008) Wave absorbing system using inclined perforated plates. J Fluid Mech 608:1–20

    Article  MathSciNet  MATH  Google Scholar 

  20. Molin B (1999) Numerical and physical wavetanks-making them fit. The twenty-second Georg Weinblum memorial lecture, Michigan

    Google Scholar 

  21. Chwang AT (1983) A porous-wavemaker theory. J Fluid Mech 132:395–406

    Article  MATH  Google Scholar 

  22. Yu X (1995) Diffraction of water waves by porous breakwaters. J Waterw Port Coast Ocean Eng 121(6):275–282

    Article  Google Scholar 

  23. Chwang AT, Wu J (1994) Wave scattering by submerged porous disk. J Eng Mech 120(12):2575–2587

    Google Scholar 

  24. Wu J, Wan Z, Fang Y (1998) Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Eng 25(9):767–779

    Article  Google Scholar 

  25. Liu Y, Li YC, Teng B, Dong S (2008) Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate. Ocean Eng 35(16):1588–1596

    Article  Google Scholar 

  26. Fang Z, Xiao L, Peng T (2017) Generalized analytical solution to wave interaction with submerged multi-layer horizontal porous plate breakwaters. J Eng Math 105(1):117–135

    Article  MathSciNet  MATH  Google Scholar 

  27. Cho IH, Kim MH (2000) Interactions of horizontal porous flexible membrane with waves. J Waterw Port Coast Ocean Eng 126(5):245–253

    Article  Google Scholar 

  28. Behera H, Sahoo T (2015) Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate. J Fluids Struct 54:643–660

    Article  Google Scholar 

  29. Williams TD, Meylan MH (2012) The Wiener-Hopf and residue calculus solutions for a submerged semi-infinite elastic plate. J Eng Math 75(1):81–106

    Article  MathSciNet  MATH  Google Scholar 

  30. Smith MJA, Peter MA, Abrahams ID, Meylan MH (2020) On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate. Proc R Soc A 476(2242):20200360

    Article  MathSciNet  Google Scholar 

  31. Elchahal G, Younes R, Lafon P (2008) The effects of reflection coefficient of the harbour sidewall on the performance of floating breakwaters. Ocean Eng 35(11–12):1102–1112

    Article  Google Scholar 

  32. Goda Y (2010) Random seas and design of maritime structures. World Scientific, Singapore

    Book  MATH  Google Scholar 

  33. Molin B, Remy F (2015) Inertia effects in TLD sloshing with perforated screens. J Fluids Struct 59:165–177

    Article  Google Scholar 

  34. Liu Y, Li HJ (2017) Iterative multi-domain BEM solution for water wave reflection by perforated caisson breakwaters. Eng Anal Bound Elem 77:70–80

    Article  MathSciNet  MATH  Google Scholar 

  35. Lee JF, & Liu CC (1995). A new solution of waves passing a submerged porous structure. In: Proceedings of the 17th International Conference on Coastal Engineering, pp 593–606

  36. Linton CM, McIver P (2001) Handbook of mathematical techniques for wave/structure interactions. CRC Press

    Book  MATH  Google Scholar 

  37. Isaacson M, Qu S (1990) Waves in a harbour with partially reflecting boundaries. Coast Eng 14(3):193–214

    Article  Google Scholar 

  38. Suh KD, Ji CH, Kim BH (2011) Closed-form solutions for wave reflection and transmission by vertical slotted barrier. Coast Eng 58(12):1089–1096

    Article  Google Scholar 

  39. Huang Z, Li Y, Liu Y (2011) Hydraulic performance and wave loadings of perforated/slotted coastal structures: a review. Ocean Eng 38(10):1031–1053

    Article  Google Scholar 

  40. Mei CC, Liu PL, Ippen AT (1974) Quadratic loss and scattering of long waves. J Waterw Harb Coast Eng Div 100(3):217–239

    Article  Google Scholar 

  41. Flagg CN, Newman JN (1971) Sway added-mass coefficients for rectangular profiles in shallow water. J Ship Res 15(04):257–265

    Article  Google Scholar 

  42. Taylor PJ (1973) The blockage coefficient for flow about an arbitrary body immersed in a channel. J Ship Res 17(02):97–105

    Article  Google Scholar 

  43. Vijay KG, Neelamani S, Sahoo T (2019) Wave interaction with multiple slotted barriers inside harbour: physical and numerical modelling. Ocean Eng 193:106623

    Article  Google Scholar 

  44. Mackay E, Johanning L (2020) Comparison of analytical and numerical solutions for wave interaction with a vertical porous barrier. Ocean Eng 199:107032

    Article  Google Scholar 

  45. Wang CD, Meylan MH (2002) The linear wave response of a floating thin plate on water of variable depth. Appl Ocean Res 24(3):163–174

    Article  Google Scholar 

  46. Vijay KG, Nishad CS, Neelamani S, Sahoo T (2021) Wave interaction with multiple wavy porous barriers using dual boundary element method. Eng Anal Bound Elem 122:176–189

    Article  MathSciNet  MATH  Google Scholar 

  47. Wang G, Ren B, Wang Y (2016) Experimental study on hydrodynamic performance of arc plate breakwater. Ocean Eng 111:593–601

    Article  Google Scholar 

Download references

Acknowledgements

This study was partially supported by the National Natural Science Foundation of China (No. 51725903). SN acknowledges the Kuwait Institute for Scientific Research for the facilities to work on this research paper.

Author information

Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao, China

    Y. Zhao & Y. Liu

  2. Oceaneering International Services Limited, Chandigarh, 160101, India

    K. G. Vijay

  3. Coastal Management Program, Environment and Life Sciences Research Centre, Kuwait Institute for Scientific Research, P.O. Box 24885, 13109, Safat, Kuwait

    S. Neelamani

Authors
  1. Y. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. G. Vijay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Neelamani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. G. Vijay.

Ethics declarations

Conflict of interest

Author declares that they have no conflict of Interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Y., Vijay, K.G., Neelamani, S. et al. Analytical study for oblique wave interaction with a submerged horizontal perforated plate near a partially reflecting vertical wall. Meccanica 56, 1751–1770 (2021). https://doi.org/10.1007/s11012-021-01339-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-021-01339-x

Keywords

Search

Navigation