Wave trapping due to composite pile-rock structure coupled with vertical barrier

Abstract

The wave transformation due to pile-rock porous structure in combination with vertical porous barrier is studied under oblique wave action. The pile-rock breakwaters consists of two rows of closely spaced piles and a rock core between them is effective in dissipating wave energy when compared with traditional rigid breakwaters due to its reduced deadweight of construction materials and additional stability. Three different cases of the vertical barrier configurations such as fully-extended barrier, bottom-standing barrier and surface-piercing barrier placed in front of the pile-rock porous structure are considered for the investigation. The numerical study is performed using the eigenfunction expansion and the associated orthogonal mode-coupling relations considering the continuity of pressure and velocity for the vertical barrier, seaward and leeward structural interfaces. The Darcy’s law is incorporated for the flow through porous media and the porosity factor of the structure is introduced using the complex porous effect parameter. The numerical results for the wave reflection, transmission and dissipation coefficient, wave force on front and rear side of porous structure along with the wave force on the barrier interface are evaluated for different hydraulic characteristics. The analysis is presented for varying structural porosity, angle of incidence, structural thickness, friction factor, length between vertical barrier and porous structure for the three different cconfigurations of vertical barrier. The numerical investigation performed in the present study will be useful for the design and analysis of the composite breakwater system to protect the offshore facility from high waves.

Keywords

Pile-rock porous structure porosity friction factor eigenfunction expansion method wave reflection wave dissipation

Get full access to this article

View all access options for this article.

References

Sollitt

Cross

. Wave transmission through permeable breakwaters. In: Proceedings of 13th international conference on coastal engineering, 1972, pp.1827–1846. New York: ASCE.

Dalrymple

Losada

Martin

. Reflection and transmission from porous structures under oblique wave attack. J Fluid Mech 1991; 224: 625–644.

Rojanakamthorn

Isobe

Watanabe

. A mathematical model of wave transformation over a submerged breakwater. Coastal Engineering 1989; 32(2): 209–234.

Twu

Chieu

. A highly wave dissipation offshore breakwater. Ocean Eng 2000; 27(3): 315–330.

Sahoo

Lee

Chwang

. Trapping and generation of waves by vertical porous structures. J Eng Mech 2000; 126(10): 1074–1082.

Liu

. Analysis of wave performance through pile–rock breakwaters. Proc IMechE, Part M: J Engineering for the Maritime Environment 2014; 228(3): 284–292.

Venkateswarlu

Karmakar

. Numerical investigation on the wave dissipating performance due to multiple porous structures. ISH J Hydraulic Eng 2021; 27(Supp. 1): 202–219.

Venkateswarlu

Karmakar

. Wave transformation due to barrier-rock porous structure placed on step-bottom. Ships Offshore Struct 2020; 15(8): 895–909.

Hayashi

Hattori

Kano

, et al. Hydraulic research on the closely spaced pile breakwater. Coast Eng J 1966; 9(1): 107–117.

10.

Chwang

. A porous-wavemaker theory. J Fluid Mech 1983; 132: 395–406.

11.

Kriebel

. Vertical wave barriers: wave transmission and wave forces. In: Proceedings of 23rd international conference on coastal engineering, 1993, pp.1313–1326. New York: ASCE.

12.

Kakuno

Liu

PL-

. Scattering of water waves by vertical cylinders. J Waterway Port Coast Ocean Eng 1993; 119(3): 302–322.

13.

Chwang

. Wave motion through porous structures. J Eng Mech 1994; 120(5): 989–1008.

14.

Mani

Jayakumar

. Wave transmission by suspended pipe breakwater. J Waterway Port Coast Ocean Eng 1995; 121: 335–338.

15.

Herbich

Douglas

. Wave transmission through a double-row pile breakwater. In: Proceedings of the 21st coastal engineering conference. Costa del Sol Malaga, Spain, 20–25 June 1988, pp. 2229–2241. New York: ASCE.

16.

Huang

. An experimental study of wave scattering by a vertical slotted barrier in the presence of a current. Ocean Eng 2007; 34(5-6): 717–723.

17.

Liu

. A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness. Ocean Eng 2012; 42: 83–92.

18.

Liu

. Analysis of oblique wave interaction with a submerged perforated semi-circular breakwater. J Eng Math 2013; 83(1): 23–36.

19.

Liu

. Analytical study of oblique wave scattering by a submerged pile–rock breakwater. Proc IMechE Part M: J Engineering for the Maritime Environment 2019; 233(1): 41–54.

20.

Suh

Kim

. An empirical formula for friction coefficient of a perforated wall with vertical slits. Coast Eng 2011; 58(1): 85–93.

21.

Karmakar

Guedes Soares

. Wave transformation due to multiple bottom-standing porous barriers. Ocean Eng 2014; 80: 50–63.

22.

Karmakar

Guedes Soares

. Propagation of gravity waves past multiple bottom-standing barriers. J Offshore Mech Arctic Eng 2015; 137(1): 1–10. 011101.

23.

Koley

Sarkar

Sahoo

. Interaction of gravity waves with bottom-standing submerged structures having perforated outer-layer placed on a sloping bed. Appl Ocean Res 2015; 52: 245–260.

24.

Venkateswarlu

Karmakar

. Wave motion over stratified porous absorber combined with seaward vertical barrier. Journal of Engineering for Maritime Environment-Part-M 2020; 234(4): 830–845.

25.

Krishna

KRA

Venkateswarlu

Karmakar

. Wave transformation due to a submerged porous block associated with a vertical barrier. In: Proceedings of 10th international conference on Asian and Pacific coasts, 2019, pp.717–724. Springer Nature.

26.

Isaacson

Baldwin

Allyn

, et al. Wave interactions with perforated breakwater. J Waterway Port Coast Ocean Eng 2000; 126(5): 229–235.

27.

Yip

Chwang

. Perforated wall breakwater with internal horizontal plate. J Eng Mech 2000; 126(5): 533–538.

28.

Chwang

Chan

. Interaction between porous media and wave motion. Annu Rev Fluid Mech 1998; 30(1): 53–84.