Wave Energy Damping due to Coupled Porous Structure and Submerged Porous Plate

Abstract

The present study investigates the wave-damping characteristics due to the combination of bottom-standing porous structure, submerged porous plate, and fully-extended porous structure of finite width using the small amplitude wave theory. The hydrodynamic characteristics such as reflection, transmission, and dissipation coefficients are determined to analyse the wave energy dissipation by the composite breakwater using the matched eigenfunction expansion method and orthogonal mode-coupling relation. Darcy’s law is incorporated to the flow through porous media. The composite breakwater system is investigated experimentally to validate and compare the numerical results with the physical model study. The complex porous effect parameter for the submerged plate is incorporated in the numerical analysis, which represents the reactance and resistance of the porous structure. The wave forces on the submerged plate and porous structure for the composite breakwater are investigated by considering the effects of changing parameters such as structural porosity, plate submergence, angle of incidence, width of the submerged porous structure and distance between the structures. The study illustrates that the increasing width of the fully-extended porous structure improves the performance of the breakwater system. The proposed study on the composite breakwater yields an useful information for wave energy attenuation, which can be designed and implemented in coastal and harbour areas to achieve wave tranquillity.

Keywords

Fully-extended porous structure / Wave transmission / Energy dissipation / Porosity / Submerged horizontal porous plate

References

[1] Arunachalam VM. Experimental studies on a perforated horizontal floating plate breakwater. Ocean Engineering, 1982, 9(1): 3545

[2] Bennett GS, McIver P, Smallman JV. A mathematical model of a slotted wavescreen breakwater. Coastal Engineering, 1992, 18(3–4): 231-249

[3] Cho IH, Kim MH. Transmission of oblique incident waves by a submerged horizontal porous plate. Ocean Engineering, 2013, 61: 56-65

[4] Cho IH, Koh HJ, Kim JR, Kim MH. Wave scattering by dual submerged horizontal porous plates. Ocean Engineering, 2013, 73: 149-158

[5] Dalrymple A, Losada A, Martin PA. Reflection and transmission from porous structure under oblique wave attack. Journal of Fluid Mechanics, 1991, 224: 625-644

[6] Das S, Bora SN. Reflection of oblique ocean water waves by a vertical rectangular porous structure placed on an elevated horizontal bottom. Ocean Engineering, 2014, 82: 135-143

[7] Dattatri J, Shankar NJ, Raman H. Performance characteristics of submerged breakwaters. Coastal Engineering, 1978, 130: 2153-2171

[8] Dick TM, Brebner A. Solid and permeable submerged breakwaters. Coastal Engineering, 1968, 72: 1141-1158

[9] Goda Y, Suzuki Y (1976) Estimation of incident and reflected waves in random wave experiments. Proceedings of 15^th Costal Engineering Conference (ASCE), Honolulu, 828–845. https://doi.org/10.1061/9780872620834.048

[10] Huang LH, Chao HI. Reflection and transmission of water wave by porous breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering, 1992, 118: 437-452

[11] Isaacson M. Measurement of regular wave reflection. Journal of Waterway, Port, Coastal, Ocean Engineering, 1991, 117: 553-569

[12] Koley S, Behera H, Sahoo T. Interaction of gravity waves with bottom standing submerged structures having perforated outer-layer placed on a sloping bed. Applied Ocean Research, 2015, 52: 245-260

[13] Li AJ, Liu Y, Fang H. Novel analytical solutions without finding complex roots for oblique wave scattering by submerged porous/perforated structures. Applied Ocean Research, 2021, 112: 102685

[14] Liu Y, Li Y. An alternative analytical solution for water-wave motion over a submerged horizontal porous plate. Journal of Engineering Mechanics, 2011, 69: 385-400

[15] Losada IJ, Dalrymple RA, Losada MA. Water waves on rown breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering, 1991, 119(4): 367-380

[16] Losada IJ, Losada MA, Martin FL. Experimental study of wave induced flow in a porous structure. Coastal Engineering, 1995, 26: 77-98

[17] Losada IJ, Silva R, Losada MA. 3-D non-breaking regular wave interaction with submerged breakwaters. Coastal Engineering, 1996, 28: 229-248

[18] Madsen Wave reflection from a vertical permeable wave absorber. Coastal Engineering, 1983, 7: 381-396

[19] Mohapatra SC, Sahoo T, Guedes Soares C. Surface gravity wave interaction with a submerged horizontal flexible porous plate. Applied Ocean Research, 2018, 78: 61-74

[20] Neelamani S, Gayathri T. Wave interaction with twin plate wave barrier. Ocean Engineering, 2006, 33(3–4): 495-516

[21] Neelamani S, Reddy MS. Wave transmission and reflection characteristics of a rigid surface and submerged horizontal plate. Ocean Engineering, 1992, 19(4): 327-341

[22] Patil SB, Karmakar D. Hydrodynamic analysis of floating tunnel with submerged rubble mound breakwater. Ocean Engineering, 2022, 264: 112460

[23] Sollitt CK, Cross RH. Wave transmission through permeable breakwaters. Coastal Engineering, 1972, 103: 1827-1846

[24] Somervell LT, Thampi SG, Shashikala AP. Estimation of friction coefficient of double walled permeable vertical breakwater. Ocean Engineering, 2018, 156: 25-37

[25] Sulisz W. Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coastal Engineering, 1985, 9: 371-386

[26] Ting CL, Lin MC, Cheng CY. Porosity effects on nonbreaking surface waves over permeable submerged breakwaters. Coastal Engineering, 2004, 50: 213-224

[27] Twu SW, Chieu CC. A highly wave dissipation offshore breakwater. Ocean Engineering, 2000, 27: 315-330

[28] Twu SW, Liu CC, Hsu WH. Wave damping characteristics of deeply submerged breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering, 2002, 127: 97-105

[29] Venkateswarlu V, Karmakar D. Significance of seabed characteristics on wave transformation in the presence of stratified porous block. Coastal Engineering Journal, 2020, 62(1): 1-22

[30] Venkateswarlu V, Karmakar D. Numerical investigation on the wave dissipating performance due to multiple porous structures. ISH Journal of Hydraulic Engineering, 2021, 27(S1): 202-219

[31] Wang HY, Sun ZC. Experimental study of a porous floating breakwater. Ocean Engineering, 2010, 37: 520-527

[32] Xie JJ. Long wave reflection by an array of submerged trapezoidal breakwaters on a sloping seabed. Ocean Engineering, 2022, 252: 111138

[33] Yang Z, Yong L, Huajun LI, Anteng C. Oblique wave motion over multiple submerged porous bars near a vertical wall. Journal of Ocean University China, 2017, 16(4): 568-574

[34] Zhu S, Chwang AT. Analytical study of porous wave absorber. Journal of Engineering Mechanics, 2001, 127: 326-332