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Oblique wave propagation through composite permeable porous structures

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Abstract

In the present study, the porous breakwater system consisting of a porous block and a permeable barrier is analysed to understand the wave dissipation due to the composite porous structure. The linearised wave theory is adopted to analyse the wave interaction with three different configurations of the composite structures including (a) porous structure and fully extended vertical barrier, (b) porous structure and bottom-standing barrier and (c) porous structure and surface-piercing barrier. The eigenfunction expansion method along with orthogonal mode-coupling relation is adopted to determine the wave reflection and transmission characteristics along with wave force on the porous structure and barrier, and surface deflection in incident and transmitted region. The experimental investigation is performed for the composite breakwater system and the results obtained are compared and validated with the numerical results. The composite breakwater system is studied for various parameters such as relative water depth, porosity of structure and barrier, structural thickness to wavelength ratio, water depth to wavelength ratio and gap between the structure and barrier. Further, the comparative study is performed with the results available in the literatures. The proposed study exhibits an informative result for the wave energy attenuation by the composite breakwater system which can be designed and implemented in coastal and harbour regions for achieving the tranquillity.

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Data Availability

No data, models, or code were generated or used during the study.

Abbreviations

\(C_{\text{m}}\) :

Coefficient of added mass

\(C_{\text{f}}\) :

Turbulent-resistant coefficient

\(d\) :

Width of the porous structure

\(\varepsilon_{\text{b}}\) :

Porosity of the barrier

\(\varepsilon_{\text{S}}\) :

Porosity of the structure

\(f_{\text{S}}\) :

Resistance coefficient of porous structure

\(f_{\text{b}}\) :

Resistance coefficient of porous barrier

\(G_{\text{b}}\) :

Porous effect parameter of barrier

\(g\) :

Acceleration due to gravity

\(h\) :

Water depth

\(h_{1}\) :

Depth of barrier from mean free surface

\(i\) :

Imaginary number

\(K_{\text{d}}\) :

Energy dissipation coefficient

\(k_{\text{jn}}\) :

Wave number in x-direction

\(K_{\text{r}}\) :

Reflection coefficient

\(K_{\text{t}}\) :

Transmission coefficient

\(L\) :

Wavelength of incident wave

\(l\) :

Wave number in z-direction

\(N\) :

Number of evanescent wave modes

\(q\) :

Instantaneous Eulerian velocity vector

\(s_{\text{s}}\) :

Reactance coefficient of porous structure

\(s_{\text{b}}\) :

Reactance coefficient of porous barrier

\(V\) :

Volume

\(w\) :

Width between the structure and barrier

\(\omega\) :

Wave frequency

\(\gamma_{\text{jn}}\) :

Wave number in y-direction

\(\theta\) :

Incident wave angle

\(\rho\) :

Density of water

\(\nu\) :

Kinematic viscosity

\(\phi\) :

Velocity potential

\(\Lambda_{\text{p}}\) :

Intrinsic permeability

References

  1. V. Venkateswarlu, D. Karmakar, Wave scattering by vertical porous block placed over flat and elevated seabed. Marine Syst. Ocean Technol. 14(2–3), 85–109 (2019)

    Article  Google Scholar 

  2. O.S. Madsen, Wave transmission through porous structures. J. Waterw. Harb. Coast. Eng. Div. 100(3), 169–188 (1974)

    Article  Google Scholar 

  3. C.K. Sollitt, R.H. Cross, Wave transmission through permeable breakwaters, in Coastal Engineering (1972), pp. 1827–1846.

  4. W. Sulisz, Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coast. Eng. 9(4), 371–386 (1985)

    Article  Google Scholar 

  5. R.A. Dalrymple, M.A. Losada, P.A. Martin, Reflection and transmission from porous structures under oblique wave attack. J. Fluid Mech. 224, 625–644 (1991)

    Article  MATH  Google Scholar 

  6. X. Yu, A.T. Chwang, Wave motion through porous structures. J. Eng. Mech. 120(5), 989–1008 (1994)

    Google Scholar 

  7. Y. Liu, H.J. Li, Wave reflection and transmission by porous breakwaters: a new analytical solution. Coast. Eng. 78, 46–52 (2013)

    Article  Google Scholar 

  8. P.A. Madsen, Wave reflection from a vertical permeable wave absorber. Coast. Eng. 7(4), 381–396 (1983)

    Article  Google Scholar 

  9. V. Mallayachari, V. Sundar, Reflection characteristics of permeable seawalls. Coast. Eng. 23(1–2), 135–150 (1994)

    Article  Google Scholar 

  10. V. Venkateswarlu, D. Karmakar, Significance of seabed characteristics on wave transformation in the presence of stratified porous block. Coast. Eng. J. 62(1), 1–22 (2020)

    Article  Google Scholar 

  11. S. Zhu, A.T. Chwang, Analytical study of porous wave absorber. J. Eng. Mech. 127(4), 326–332 (2001)

    Google Scholar 

  12. J.E. Burke, Scattering of surface waves on an infinitely deep fluid. J. Math. Phys. 5(6), 805–819 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  13. C.C. Mei, Radiation and scattering of transient gravity waves by vertical plates. Quart. J. Mech. Appl. Math. 19(4), 417–440 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  14. C.C. Mei, J.L. Black, Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38(3), 499–511 (1969)

    Article  MATH  Google Scholar 

  15. E.O. Tuck, Transmission of water waves through small apertures. J. Fluid Mech. 49(1), 65–74 (1971)

    Article  MATH  Google Scholar 

  16. D.V. Evans, A note on the waves produced by the small oscillations of a partially immersed vertical plate. IMA J. Appl. Math. 17(2), 135–140 (1976)

    Article  MATH  Google Scholar 

  17. D. Porter, The radiation and scattering of surface waves by vertical barriers. J. Fluid Mech. 63(4), 625–634 (1974)

    Article  MATH  Google Scholar 

  18. C. Macaskill, Reflexion of water waves by a permeable barrier. J. Fluid Mech. 95(1), 141–157 (1979)

    Article  MATH  Google Scholar 

  19. D.L. Kriebel, Vertical wave barriers: wave transmission and wave forces, in Coastal Engineering (1993), pp. 1313–1326.

  20. S. Urashima, K. Ishizuka, H. Kondo, Energy dissipation and wave force at slotted wall, in Coastal Engineering (1986), pp. 2344–2352.

  21. I.J. Losada, M.A. Losada, A.J. Roldán, Propagation of oblique incident waves past rigid vertical thin barriers. Appl. Ocean Res. 14(3), 191–199 (1992)

    Article  Google Scholar 

  22. T. Sahoo, M.M. Lee, A.T. Chwang, Trapping and generation of waves by vertical porous structures. J. Eng. Mech. 126(10), 1074–1082 (2000)

    Google Scholar 

  23. D. Karmakar, C. Guedes Soares, Wave transformation due to multiple bottom-standing porous barriers. Ocean Eng. 80, 50–63 (2014)

    Article  Google Scholar 

  24. D. Karmakar, C. Guedes Soares, Propagation of gravity waves past multiple bottom-standing barriers. J. Offshore Mech. Arct. Eng. 137(011101), 1–10 (2015)

    Google Scholar 

  25. R.B. Kaligatla, S. Tabssum, T. Sahoo, Effect of bottom topography on wave scattering by multiple porous barriers. Meccanica 53(4–5), 887–903 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  26. M.S. Kirkgöz, Impact pressure of breaking waves on vertical and sloping walls. Ocean Eng. 18(1–2), 45–59 (1991)

    Article  Google Scholar 

  27. M. Fugazza, L. Natale, Hydraulic design of perforated breakwaters. J. Waterw. Port Coast. Ocean Eng. 118(1), 1–14 (1992)

    Article  Google Scholar 

  28. C.P. Tsai, C.H. Yu, H.B. Chen, H.Y. Chen, Wave height transformation and set-up between a submerged permeable breakwater and a seawall. China Ocean Eng. 26(1), 167–176 (2012)

    Article  Google Scholar 

  29. S. Koley, A. Sarkar, T. Sahoo, Interaction of gravity waves with bottom-standing submerged structures having perforated outer-layer placed on a sloping bed. Appl. Ocean Res. 52, 245–260 (2015)

    Article  Google Scholar 

  30. F. He, Z. Huang, Hydrodynamic performance of pile-supported OWC-type structures as breakwaters: an experimental study. Ocean Eng. 88, 618–626 (2014)

    Article  Google Scholar 

  31. D. Karmakar, T. Sahoo, Gravity wave interaction with floating membrane due to change in water depth. Ocean Eng. 35(7), 598–615 (2008)

    Article  Google Scholar 

  32. Z. Huang, An experimental study of wave scattering by a vertical slotted barrier in the presence of a current. Ocean Eng. 34(5–6), 717–723 (2007)

    Article  Google Scholar 

  33. P.L.F. Liu, M. Iskandarani, Scattering of short-wave groups by submerged horizontal plate. J. Waterw. Port Coast. Ocean Eng. 117(3), 235–246 (1991)

    Article  Google Scholar 

  34. M. Patarapanich, Maximum and zero reflection from submerged plate. J. Waterw. Port Coast. Ocean Eng. 110(2), 171–181 (1984)

    Article  Google Scholar 

  35. H. Behera, T. Sahoo, C.O. Ng, Wave scattering by a partial flexible porous barrier in the presence of step-type bottom topography. Coast. Eng. J. 58(3), 1–26 (2016)

    Article  Google Scholar 

  36. R. Gayathri, P. Kar, H. Behera, T. Sahoo, Oblique wave scattering by a floating bridge in the presence of a vertical permeable flexible barrier. J. Offshore Mech. Arct. Eng. 143(2), 021701-1–17 (2021)

    Article  Google Scholar 

  37. R. Gayathri, M.B.M. Khan, H. Behera, Attenuation of wave force on a floating dock by multiple porous breakwaters. Eng. Anal. Bound. Elem. 143, 170–189 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  38. R.B. Kaligatla, M. Sharma, T. Sahoo, Wave interaction with a pair of submerged floating tunnels in the presence of an array of submerged porous breakwaters. J. Offshore Mech. Arct. Eng. 143(2), 021402-1–14 (2021)

    Article  Google Scholar 

  39. M. Isaacson, Measurement of regular wave reflection. J. Waterway Port Coast. Ocean Eng. 117, 553–569 (1991)

    Article  Google Scholar 

  40. Y. Goda, Y. Suzuki, Estimation of incident and reflected waves in random wave experiments, in Proceedings of 15th Costal Engineering Conference (ASCE), Honolulu (1976), pp. 828 – 845.

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Acknowledgements

The authors are thankful to NITK Surathkal and Ministry of Education, New Delhi, for providing financial and necessary support to perform the research work.

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  1. Department of Water Resources and Ocean Engineering, National Institute of Technology Karnataka, Surathkal, Mangaluru, 575025, India

    K. R. Athul Krishna, Abhishek G. Karaseeri & D. Karmakar

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  1. K. R. Athul Krishna
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Krishna, K.R.A., Karaseeri, A.G. & Karmakar, D. Oblique wave propagation through composite permeable porous structures. Mar Syst Ocean Technol 17, 164–187 (2023). https://doi.org/10.1007/s40868-022-00122-1

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