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

Anjan Sasmal , Sandip Paul , Soumen De

Journal of Marine Science and Application ›› 2019, Vol. 18 ›› Issue (4) : 417 -432.

PDF
Journal of Marine Science and Application ›› 2019, Vol. 18 ›› Issue (4) : 417 -432. DOI: 10.1007/s11804-019-00107-4
Research Article

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

Author information +
History +
PDF

Abstract

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.

Keywords

Water wave scattering / Galerkin approximation / Porosity / Two unequal barriers / Reflection and transmission coefficients

Cite this article

Download citation ▾
Anjan Sasmal, Sandip Paul, Soumen De. Effect of Porosity on Oblique Wave Diffraction by Two Unequal Vertical Porous Barriers. Journal of Marine Science and Application, 2019, 18(4): 417-432 DOI:10.1007/s11804-019-00107-4

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Banerjea S, Kanoria M, Dolai DP, Mandal BN. Oblique wave scattering by a submerged thin wall with gap in finite depth water. Appl Ocean Res, 1996, 18: 319-327

[2]

Behera H, Sahoo T. Gravity wave interaction with porous structures in two-layer fluid. J Eng Math, 2014, 87(1): 73-97

[3]

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

[4]

Chwang AT. A porous wave maker theory. J Fluid Mech, 1983, 132: 395-406

[5]

Das S, Bora SN. Oblique water wave damping by two submerged thin vertical porous plates of different heights. Comput Appl Math, 2018, 37(3): 3759-3779

[6]

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)

[7]

De S, Mandal BN, Chakrabarti A. Use of abel integral equations in water wave scattering by two surface piercing barriers. Wave Motion, 2010, 47: 279-288

[8]

Dean WR. On the reflection of surface waves by a flat plate floating vertically. Math Proc Camb Philos Soc, 1945, 41: 231-238

[9]

Evans DV. Diffraction of water waves by a submerged vertical plate. J Fluid Mech, 1970, 40: 433-451

[10]

Evans DV, Morris CAN. Complementary approximations to the solution of a problem in water waves. J Inst Math Applications, 1972, 10(1): 1-9

[11]

Gayen R, Mondal A. A hypersingular integral equation approach to the porous plate problem. Appl Ocean Res, 2014, 46: 70-78

[12]

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)

[13]

Isaacson M, Baldwin J, Premasiri S, Yang G. Wave interactions with double slotted barriers. Appl Ocean Res, 1999, 21: 81-91

[14]

Jarvis RJ. The scattering of surface waves by two vertical plane barriers. J Inst Maths Applic, 1971, 7: 207-215

[15]

Kanoria M, Mandal BN. Oblique wave diffraction by two parallel vertical barriers with submerged gaps in water of uniform finite depth. J Tech Phys, 1996, 37: 187-204

[16]

Karmakar D, Guedes Soares C. Wave transmission due to multiple bottom-standing porous barriers. Ocean Eng, 2014, 80: 50-63

[17]

Karp NS, Karal CF. The elastic field behaviour in the neigh-bourhood of a crack of arbitrary angle. Commun Pure Appl Math, 1962, 15: 413-421

[18]

Lee MM, Chwang AT. Scattering and radiation of water waves by permeable barriers. Phys Fluids, 2000, 12: 54-65

[19]

Levine H, Rodemich E, 1969. Scattering of surface waves on an ideal fluid, Tech rep, DTIC Document

[20]

Li AJ, Liu Y, Li HJ. Accurate solutions to water wave scattering by vertical thin porous barriers. Math Probl Eng, 2015, 2015: 1-11

[21]

Macaskill C. Reflection of water waves by a permeable barrier. J Fluid Mech, 1979, 75: 141-157

[22]

Manam SR, Sivanesan M. Scattering of water waves by vertical porous barriers: an analytical approach. Wave Motion, 2016, 67: 89-101

[23]

Mandal BN, Chakrabarti A. Water wave scattering by barriers, 2000, Southampton: WIT Press, 24-25

[24]

McIver P. Scattering of surface waves by two surface piercing vertical barriers. IMA J Appl Math, 1985, 35(1): 1-17

[25]

Mohapatra SC, Sahoo T, Guedes Soares C. Surface gravity wave interaction with a submerged horizontal flexible porous plate. Appl Ocean Res, 2018, 78: 61-74

[26]

Newman JN. Interaction of water waves with two closely spaced vertical obstacles. J Fluid Mech, 1974, 66: 97-106

[27]

Porter R, Evans DV. Complementary approximations to wave scattering by vertical barriers. J Fluid Mech, 1995, 294: 155-180

[28]

Roy R, Basu U, Mandal BN. Oblique water scattering by two unequal vertical barriers. J Eng Math, 2016, 97: 119-133

[29]

Sollitt CK, Cross RH. Wave transmission through permeable breakwaters. Coast Eng Proc, 1972, 1: 1827-1846

[30]

Ursell F. The effect of a fixed vertical barrier on surface waves in deep water. Math Proc Camb Philos Soc, 1947, 43: 374-382

[31]

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)

AI Summary AI Mindmap
PDF

155

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/