Abstract
The interaction between oblique surface waves and multiple bottom-standing flexible porous barriers under the combined effects of a neighboring rigid vertical wall and a step of arbitrary profile on the bottom is investigated. The problem is analyzed under the assumptions of small-amplitude water waves and structural response. The solutions are found using the methods of least-squares approximation, eigenfunction expansion and multi-mode approximation associated with the modified mild-slope equation. To keep the barriers at a desired position of interest, clamped-free or clamped-moored edge conditions are considered. Effects of various wave and structural parameters are studied for single, double and multiple barriers by looking into the reflection coefficient, wave force exerted on the rigid wall, free-surface elevations, and plate deflection of the barriers. The model is validated by comparing with results available in the literature for the special case of wave interaction with single and double rigid porous barriers near a rigid wall in the presence of a vertical step. The study reveals that the presence of multiple flexible porous barriers may effectively reduce the wave reflection and wave force exerted on the rigid wall. Further, full and nearly zero wave reflection can be found in the case of single and/or multiple barriers.
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References
Jarlan G (1961) A perforated vertical wall breakwater. Dock Harb Auth 41(486):394–398
Suh KD, Park WS (1995) Wave reflection from perforated-wall caisson breakwaters. Coast Eng 26(3):177–193
Sahoo T, Lee M, Chwang A (2000) Trapping and generation of waves by vertical porous structures. J Eng Mech 126(10):1074–1082
Li Y, Dong G, Liu H, Sun D (2003) The reflection of oblique incident waves by breakwaters with double-layered perforated wall. Coast Eng 50(1):47–60
Teng B, Zhang X, Ning D (2004) Interaction of oblique waves with infinite number of perforated caissons. Ocean Eng 31(5):615–632
Liu Y, Li Y-C, Teng B (2007) The reflection of oblique waves by an infinite number of partially perforated caissons. Ocean Eng 34(14):1965–1976
Liu Y, Li Y, Teng B, Jiang J, Ma B (2008) Total horizontal and vertical forces of irregular waves on partially perforated caisson breakwaters. Coast Eng 55(6):537–552
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
Behera H, Sahoo T (2014) Gravity wave interaction with porous structures in two-layer fluid. J Eng Math 87(1):73–97
Behera H, Kaligatla R, Sahoo T (2015) Wave trapping by porous barrier in the presence of step type bottom. Wave Motion 57:219–230
Liu Y, Li Y-C, Teng B (2016) Interaction between oblique waves and perforated caisson breakwaters with perforated partition walls. Eur J Mech B Fluids 56:143–155
Yip TL, Sahoo T, Chwang AT (2002) Trapping of surface waves by porous and flexible structures. Wave Motion 35(1):41–54
Behera H, Mandal S, Sahoo T (2013) Oblique wave trapping by porous and flexible structures in a two-layer fluid. Phys Fluids (1994-present) 25(11):112110
Kaligatla R, Koley S, Sahoo T (2015) Trapping of surface gravity waves by a vertical flexible porous plate near a wall. Zeitschrift für angewandte Mathematik und Physik 66(5):2677–2702
Meylan MH (1995) A flexible vertical sheet in waves. Int J Offshore Polar Eng 5(02):105–110
Mandal BN, Chakrabarti A (2000) Water wave scattering by barriers. WIT Press/Computational Mechanics
Lee WK, Lo EY (2002) Surface-penetrating flexible membrane wave barriers of finite draft. Ocean Eng 29(14):1781–1804
Karmakar D, Bhattacharjee J, Soares CG (2013) Scattering of gravity waves by multiple surface-piercing floating membrane. Appl Ocean Res 39:40–52
Karmakar D, Soares CG (2014) Wave transformation due to multiple bottom-standing porous barriers. Ocean Eng 80:50–63
Hassan ULM, Meylan MH, Peter M (2009) Water-wave scattering by submerged elastic plates. Q J Mech Appl Math 62(3):321–344
Meylan MH, Bennetts LG, Peter MA (2017) Water-wave scattering and energy dissipation by a floating porous elastic plate in three dimensions. Wave Motion 70:240–250
Das S, Sahoo T (2017) Hydroelastic analysis of very large floating structure over viscoelastic bed. Meccanica 52(8):1871–1887
Behere H, Sahoo T, Ng C-O (2016) Wave scattering by a partial flexible porous barrier in the presence of a step-type bottom topography. Coast Eng J 58(3):1650008
Koley S, Sahoo T (2017) Oblique wave scattering by horizontal floating flexible porous membrane. Meccanica 52(1–2):125–138
Chamberlain PG, Porter D (1995) The modified mild-slope equation. J Fluid Mech 291:393–407
Porter D, Staziker D (1995) Extensions of the mild-slope equation. J Fluid Mech 300:367–382
Yu X, Chwang AT (1994) Wave motion through porous structures. J Eng Mech 120(5):989–1008
Magrab EB (1979) Vibrations of elastic structural members. Sijthoff and Noordhoff, Alphen aan den Rijn
Porter R, Porter D (2000) Water wave scattering by a step of arbitrary profile. J Fluid Mech 411:131–164
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Behera, H., Ng, CO. Interaction between oblique waves and multiple bottom-standing flexible porous barriers near a rigid wall. Meccanica 53, 871–885 (2018). https://doi.org/10.1007/s11012-017-0789-8
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DOI: https://doi.org/10.1007/s11012-017-0789-8