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 Arpita Mondal,R. Gayen.Wave Interaction with Dual Circular Porous Plates[J].Journal of Marine Science and Application,2015,(4):366-375.[doi:10.1007/s11804-015-1325-7]
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Wave Interaction with Dual Circular Porous Plates


Wave Interaction with Dual Circular Porous Plates
Arpita Mondal R. Gayen
Arpita Mondal R. Gayen
Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India
water wave scatteringcircular-arc-shaped plateshypersingular integral equationGreen’s integral theoremreflection coefficientenergy identityhydrodynamic force
In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green’s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cum-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.


Das P, Dolai DP, Mandal BN (1997). Oblique wave diffraction by parallel thin vertical barriers with gaps. Journal of Waterway, Port, Coastal, and Ocean Engineering, 123(4), 163-171. DOI: 10.1061/(ASCE)0733-950X(1997)123:4(163)
De SM, Mandal BN, Chakrabarti A (2009). Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach. Journal of Engineering Mathematics, 65(1), 75-87. DOI: 10.1007/s10665-009-9265-3
De SM, Mandal BN, Chakrabarti A (2010). Use of Abel integral equations in water wave scattering by two surface-piercing barriers. Wave Motion, 47(5), 279-288. DOI: 10.1016/j.wavemoti.2009.12.002
Evans DV (1970). Diffraction of water waves by a submerged vertical plate. Journal of Fluid Mechanics, 40(3), 433-451. DOI: 10.1017/S0022112070000253
Gayen R, Mondal A (2014). A hypersingular integral equation approach to the porous plate problem. Applied Ocean Research, 46, 70-78. DOI: 10.1016/j.apor.2014.01.006
Golberg MA (1983). The convergence of several algorithms for solving integral equations with finite-part integrals. Journal of Integral Equations, 5, 329-340.
Golberg MA (1985). The convergence of several algorithms for solving integral equations with finite-part integrals II. Journal of Integral Equations, 9, 267-275.
Isaacson M, Baldwin J, Premasiri S, Yang G (1999). Wave interactions with double slotted barriers. Applied Ocean Research, 21(2), 81-91. DOI: 10.1016/S0141-1187(98)00039-X
Jarvis RJ (1971). The scattering of surface waves by two vertical plane barriers. Journal of the Institute of Mathematics and its Applications, 7, 207-215.
Kanoria M, Mandal BN (2002). Water wave scattering by a submerged circular-arc-shaped plate. Fluid Dynamics Research, 31(5-6), 317-331. DOI: 10.1016/S0169-5983(02)00136-3
Karmakar D, Guedes Soares C (2014). Wave transformation due to multiple bottom-standing porous barriers. Ocean Engineering, 80, 50-63. DOI: 10.1016/j.oceaneng.2014.01.012
Koraim AS, Heikal EM, Rageh OS (2011). Hydrodynamic characteristics of double permeable breakwater under regular waves. Marine Structures, 24(4), 503-527. DOI: 10.1016/j.marstruc.2011.06.004
Levine H, Rodemich E (1958). Scattering of surface waves on an ideal fluid. Mathematics and Statistics Laboratory, Stanford University, Palo Alto, USA, Technical Report No.78.
Losada IJ, Losada MA, Roldán AJ (1992). Propagation of oblique incident waves past rigid vertical thin barriers. Applied Ocean Research, 14(3), 191-199. DOI: 10.1016/0141-1187(92)90014-B
Lu CJ, He YS (1989). Reflexion and transmission of water waves by a thin curved permeable barrier. Journal of Hydrodynamics, 1(3), 77-85.
Mandal BN, Chakrabarti A (2000). Water wave scattering by barriers. WIT Press, Southampton, UK.
Mandal BN, Gayen R (2002). Water-wave scattering by two symmetric circular-arc-shaped thin plates. Journal of Engineering Mathematics, 44(3), 297-309. DOI: 10.1023/A:1020944518573
Martin PA, Rizzo FJ (1989). On boundary integral equations for crack problems. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 421(1861), 341-355. DOI: 10.1098/rspa.1989.0014
McIver M, Urka U (1995). Wave scattering by circular arc shaped plates. Journal of Engineering Mathematics, 29(6), 575-589. DOI: 10.1007/BF00044123
Neelamani S, Vedagiri M (2002). Wave interaction with partially immersed twin vertical barriers. Ocean Engineering, 29(2), 215-238. DOI: 10.1016/S0029-8018(00)00061-5
Newman JN (1974). Interaction of water waves with two closely spaced vertical obstacles. Journal of Fluid Mechanics, 66(1), 97-106. DOI: 10.1017/S0022112074000085
Twu SW, Lin DT (1991). On a highly effective wave absorber. Coastal Engineering, 15(4), 389-405. DOI: 10.1016/0378-3839(91)90018-C
Parsons NF, Martin PA (1994). Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Applied Ocean Research, 16(3), 129-139. DOI: 10.1016/0141-1187(94)90024-8
Porter D (1972). The transmission of surface waves through a gap in a vertical barrier. Mathematical Proceedings of the Cambridge Philosophical Society, 71(2), 411-421. DOI: 10.1017/S0305004100050647
Ursell F (1947). The effect of a fixed vertical barrier on surface waves in deep water. Mathematical Proceedings of the Cambridge Philosophical Society, 43(3), 374-382. DOI: 10.1017/S0305004100023604
Ursell F (1950). Surface waves on deep water in the presence of a submerged circular cylinder. I. Mathematical Proceedings of the Cambridge Philosophical Society, 46(1), 141-152. DOI: 10.1017/S0305004100025561
Yu XP, Chwang AT (1994). Wave-induced oscillation in harbor with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 120(2), 125-144.DOI: 10.1061/(ASCE)0733-950X(1994)120:2(125)


基金项目:Partially Supported by the Department of Science and Technology Through a Research Grant to RG (No. SR/FTP/MS-020/2010).
通讯作者:R. Gayen, E-mail:rupanwita@maths.iitkgp.ernet.in
Last Update: 2015-11-07