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Citation:
　R. Ashok,S. R. Manam.Oblique Wave Scattering Problems Involving Vertical Porous Membranes[J].Journal of Marine Science and Application,2022,(1):51-66.[doi:10.1007/s11804-022-00255-0]
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Oblique Wave Scattering Problems Involving Vertical Porous Membranes

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Title:
Oblique Wave Scattering Problems Involving Vertical Porous Membranes
Author(s):
R. Ashok;  S. R. Manam
Affilations:
Author(s):
R. Ashok;  S. R. Manam
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
Keywords:
Free surface gravity waves; Reflection coefficient; Singular integral equation; Galerkin approximation; Linear waves; Vertical porous membrane barrier
分类号:
-
DOI:
10.1007/s11804-022-00255-0
Abstract:
Oblique surface waves incident on a fixed vertical porous membrane of various geometric configurations is analyzed here. The mixed boundary value problem is modified into easily resolvable problems by using a connection. These problems are reduced to that of solving a couple of integral equations. These integral equations are solved by a one-term or a two-term Galerkin method. The method involves a basis functions consists of simple polynomials multiplied with a suitable weight functions induced by the barrier. Coefficient of reflection and total wave energy are numerically evaluated and analyzed against various wave parameters. Enhanced reflection is found for all the four barrier configurations.

References:

Ashok R, Gunasundari C, Manam SR (2020) Explicit solutions of the scattering problems involving vertical flexible porous structures. Journal of Fluids and Structures 99:103149. https://doi.org/10.1016/j.jfluidstructs.2020.103149
Cho IH, Kim MH (1998) Interactions of a horizontal flexible membrane with oblique incident waves. Journal of Fluid Mechanics 367:139-161. https://doi:10.1017/S0022112098001499
Cho IH, Kim MH (2000) Interactions of horizontal porous flexible membrane with waves. Journal of Waterway Port Coastal and Ocean Engineering 126(5):245-253. https://doi.org/10.1061/(ASCE)0733-950X(2000)126:5(245)
Chwang AT (1983) A porous wave maker theory. J Fluid Mech 132:395-406. https://doi.org/10.1017/S0022112083001676
Das BC, De S, Mandal BN (2018a) The problem of oblique scattering by a thin vertical submerged plate in deep water revisited. Springer Proceedings in Mathematics and Statistics 253:225-236. https://doi.org/10.1007/978-981-13-2095-8_18
Das BC, De S, Mandal BN (2018b) Oblique scattering by thin vertical barriers in deep water:solution by multi-term Galerkin technique using simple polynomials as basis. J Mar Sci Technol 23:915-925. https://doi.org/10.1007/s00773-017-0520-4
Das BC, De S, Mandal BN (2019) Wave propagation through a gap in a thin vertical wall in deep water. CUBO A Mathematical Journal 21(3):93-105. http://dx.doi.org/10.4067/S0719-06462019000300093
Dean WR (1945) On the reflection of surface waves by submerged plane barrier. Proc Camb Phil Soc 41:231-238. https://doi.org/10.1017/S030500410002260X Evans DV (1970) Diffraction of water waves by a submerged vertical plate. J Fluid Mech 40:433-451. https://doi.org/10.1017/S0022112070000253
Evans DV, Morris CAN (1972) The effect of a fixed vertical barrier on obliquely incident surface waves in deep water. J Inst Maths Applies 9:198-204. https://doi.org/10.1093/imamat/9.2.198
Havelock TH (1929) Forced surface waves on water. Phil Mag Ser 8:569-576. https://doi.org/10.1080/14786441008564913
Karmakar D, Guedes Soares C (2012) Oblique scattering of gravity waves by moored floating membrane with changes in bottom topography. Ocean Engineering 54:87-100. https://doi.org/10.1016/j.oceaneng.2012.07.005
Kim MH, Kee ST (1996) Flexible-membrane wave barrier I:analytic and numerical solutions. Journal of Waterway Port Coastal and Ocean Engineering 122(1):46-53. https://doi.org/10.1061/(ASCE)0733-950X(1996)122:1(46)
Koley S, Sahoo T (2017) Oblique wave trapping by vertical permeable membrane barriers located near a wall. J Marine Sci Appl 16:490-501. https://doi.org/10.1007/s11804-017-1432-8
Lamb H (1932) Hydrodynamics. Cambridge University Press, Cambridge Lee JF, Chen CJ (1990) Wave interaction with hinged flexible breakwater. J Hydraulic Res 28:283-297. https://doi.org/10.1080/00221689009499070
Lewin M (1963) The effect of vertical barriers on progressive waves. J Math Phys 42:287-300. https://doi.org/10.1002/sapm1963421287
Manam SR, Bhattacharjee J, Sahoo T (2006) Expansion formulae in wave structure interaction problems. Proceeding of Royal Society LondonA 462(2065):263-287.https://doi.org/10.1098/rspa.2005.1562
Mandal S, Behera H, Sahoo T (2016) Oblique wave interaction with porous flexible barriers in a two-layer fluid. J Eng Math 100:1-31.https://doi.org/10.1007/s10665-015-9830-x
Mandal BN, Chakrabarti A (2000) WaterWave Scattering by Barriers.WIT Press, Southampton
Mandal BN, Das P (1996) Oblique diffraction of surface waves by a submerged vertical plate. J Engng Math 30:459-470. https://doi.org/10.1007/BF00049246
Mei CC (1966) Radiation and scattering of transient gravity waves by vertical plates. Q J Mech Appl Maths 19:417-440. https://doi.org/10.1093/qjmam/19.4.417
Selvan SA, Behera H (2020) Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids.Ocean Engineering 206:107374. https://doi.org/10.1016/j.oceaneng.2020.107374
Suresh Kumar P, Manam SR, Sahoo T (2007) Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid.Journal of Fluids and Structures 23(4):633-647. https://doi.org/10.1016/j.jfluidstructs.2006.10.011
Ursell F (1947) The effect of a fixed vertical barrier on surface waves in deep water. Proc Camb Phil Soc 43:374-382. https://doi.org/10.1017/S0305004100023604
Williams AN, Gaiger PT, McDogal WG (1991) Flexible floating breakwater. J Wateway Port Coastal Ocean Eng ASCE 117(5):429-450. https://doi.org/10.1061/(ASCE)0733-950X(1991)117:5(429)
Yip TL, Sahoo T, Chwang AT (2001) Wave scattering by multiple floating membranes. The Eleventh International Offshore and Polar Engineering Conference, 3:379-384
Yu X, Chwang AT (1994) Wave induced oscillation in harbor with porous breakwaters. J Waterway Port Coastal Ocean Eng ASCE 120(2):125-144. https://doi.org/10.1061/(ASCE)0733-950X(1994) 120:2(125)

Memo

Memo:
Received date: 2021-09-29;Accepted date: 2022-02-19。
Corresponding author:R. Ashok,E-mail:ashokkumaraswin@gmail.com
Last Update: 2022-04-22