Effect of Porosity on Oblique Wave Diffraction by Two Unequal Vertical Porous Barriers

Journal of Marine Science and Application - Tập 18 - Trang 417-432 - 2019
Anjan Sasmal1, Sandip Paul2, Soumen De1
1Department of Applied Mathematics, University of Calcutta, Kolkata, India
2Department of Mathematics, Dr. B.C.Roy Engineering College, Durgapur, India

Tóm tắt

The diffraction of obliquely incident wave by two unequal barriers with different porosity in infinitely deep water is investigated by using two-dimensional linearized potential theory. Reflection and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged barriers. The amount of energy dissipation due to the permeable barriers is derived using Green’s integral theorem. The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous barriers. The numerical results of hydrodynamics quantities are illustrated graphically.

Tài liệu tham khảo

Banerjea S, Kanoria M, Dolai DP, Mandal BN (1996) Oblique wave scattering by a submerged thin wall with gap in finite depth water. Appl Ocean Res 18:319–327. https://doi.org/10.1016/S0141-1187(97)00002-3 Behera H, Sahoo T (2014) Gravity wave interaction with porous structures in two-layer fluid. J Eng Math 87(1):73–97. https://doi.org/10.1007/s10665-013-9667-0 Bhattacharjee J, Guedes Soares C, (2011) Vertical porous membrane barrier for coastal structure near a wall, Coastal and Maritime Mediterranean Conference, Edition 2, Tanger, Maroc, 15–20. DOI: https://doi.org/10.5150/cmcm.2011.004 Chwang AT (1983) A porous wave maker theory. J Fluid Mech 132:395–406. https://doi.org/10.1017/S0022112083001676 Das S, Bora SN (2018) Oblique water wave damping by two submerged thin vertical porous plates of different heights. Comput Appl Math 37(3):3759–3779. https://doi.org/10.1007/s40314-017-0545-7 Das P, Dolai DP, Mandal BN (1997) Oblique wave diffraction by parallel thin vertical barriers with gaps. J Waterw Port Coast Ocean Eng 123:163–171. https://doi.org/10.1061/(ASCE)0733-950X(1997)123:4(163) De S, Mandal BN, Chakrabarti A (2010) Use of abel integral equations in water wave scattering by two surface piercing barriers. Wave Motion 47:279–288. https://doi.org/10.1016/j.wavemoti.2009.12.002 Dean WR (1945) On the reflection of surface waves by a flat plate floating vertically. Math Proc Camb Philos Soc 41:231–238 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) Complementary approximations to the solution of a problem in water waves. J Inst Math Applications 10(1):1–9. https://doi.org/10.1093/imamat/10.1.1 Gayen R, Mondal A (2014) A hypersingular integral equation approach to the porous plate problem. Appl Ocean Res 46:70–78. https://doi.org/10.1016/j.apor.2014.01.006 Isaacson M, Premasiri S, Yang G (1998) Wave interactions with vertical slotted barriers, J. Waterw Port Coast Ocean Eng 124:118–126. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:3(118) Isaacson M, Baldwin J, Premasiri S, Yang G (1999) Wave interactions with double slotted barriers. Appl Ocean Res 21:81–91. https://doi.org/10.1016/S0141-1187(98)00039-X Jarvis RJ (1971) The scattering of surface waves by two vertical plane barriers. J Inst Maths Applic 7:207–215 Kanoria M, Mandal BN (1996) Oblique wave diffraction by two parallel vertical barriers with submerged gaps in water of uniform finite depth. J Tech Phys 37:187–204 Karmakar D, Guedes Soares C (2014) Wave transmission due to multiple bottom-standing porous barriers. Ocean Eng 80:50–63. https://doi.org/10.1016/j.oceaneng.2014.01.012 Karp NS, Karal CF (1962) The elastic field behaviour in the neigh-bourhood of a crack of arbitrary angle. Commun Pure Appl Math 15:413–421. https://doi.org/10.1002/cpa.3160150404 Lee MM, Chwang AT (2000) Scattering and radiation of water waves by permeable barriers. Phys Fluids 12:54–65. https://doi.org/10.1063/1.870284 Levine H, Rodemich E, 1969. Scattering of surface waves on an ideal fluid, Tech rep, DTIC Document Li AJ, Liu Y, Li HJ (2015) Accurate solutions to water wave scattering by vertical thin porous barriers. Math Probl Eng 2015:1–11. https://doi.org/10.1155/2015/985731 Macaskill C (1979) Reflection of water waves by a permeable barrier. J Fluid Mech 75:141–157. https://doi.org/10.1017/S0022112079001385 Manam SR, Sivanesan M (2016) Scattering of water waves by vertical porous barriers: an analytical approach. Wave Motion 67:89–101. https://doi.org/10.1016/j.wavemoti.2016.07.008 Mandal BN, Chakrabarti A (2000) Water wave scattering by barriers. WIT Press, Southampton, pp 24–25 McIver P (1985) Scattering of surface waves by two surface piercing vertical barriers. IMA J Appl Math 35(1):1–17. https://doi.org/10.1093/imamat/35.3.339 Mohapatra SC, Sahoo T, Guedes Soares C (2018) Surface gravity wave interaction with a submerged horizontal flexible porous plate. Appl Ocean Res 78:61–74. https://doi.org/10.1016/j.apor.2018.06.002 Newman JN (1974) Interaction of water waves with two closely spaced vertical obstacles. J Fluid Mech 66:97–106. https://doi.org/10.1017/S0022112074000085 Porter R, Evans DV (1995) Complementary approximations to wave scattering by vertical barriers. J Fluid Mech 294:155–180. https://doi.org/10.1017/S0022112095002849 Roy R, Basu U, Mandal BN (2016) Oblique water scattering by two unequal vertical barriers. J Eng Math 97:119–133. https://doi.org/10.1007/s10665-015-9800-3 Sollitt CK, Cross RH (1972) Wave transmission through permeable breakwaters. Coast Eng Proc 1:1827–1846. https://doi.org/10.1061/9780872620490.106 Ursell F (1947) The effect of a fixed vertical barrier on surface waves in deep water. Math Proc Camb Philos Soc 43:374–382. https://doi.org/10.1017/S0305004100023604 Yu X (1995) Diffraction of water waves by porous breakwaters, J. Waterw Port Coast Ocean Eng 121:275–282. https://doi.org/10.1061/(ASCE)0733-950X(1995)121:6(275)