|Table of Contents|

 Saista Tabssum,Balaji Ramakrishnan.Oblique Wave Interaction With Flexible Plate in Ocean of Uneven Bottom[J].Journal of Marine Science and Application,2024,(2):261-275.[doi:10.1007/s11804-024-00395-5]
Click and Copy

Oblique Wave Interaction With Flexible Plate in Ocean of Uneven Bottom


Oblique Wave Interaction With Flexible Plate in Ocean of Uneven Bottom
Saista Tabssum1 Balaji Ramakrishnan2
Saista Tabssum1 Balaji Ramakrishnan2
1 School of Advanced Science-Mathematics, VIT-AP, Amravati, 744101, India;
2 Department of Civil Engineering, Indian Institute of Technology, Bombay 400076, India
Porous flexible breakwater|Varying bottom|Mild-slope equation|Reflection coefficient|Wave force
The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom. The physical models for both scattering and trapping cases are considered and developed within the framework of small amplitude water-wave theory. Darcy’s law is used to model the wave interaction with the porous medium. It is assumed that the varying bottom extends over a finite interval, connected by a finite length of uniform bottom near an impermeable wall, and a semi-infinite length of bottom in the open water region. The boundary value problem is solved using the eigenfunction expansion method in the uniform bottom regions, while a modified mild-slope equation (MMSE) is used for the region with the varying bottom. Additionally, a mass-conserving jump condition is employed to handle the solution at slope discontinuities in the bottom. A system of equations is derived by matching the solutions at interfaces. The reflection coefficient and force on the breakwater and impermeable wall are plotted and analyzed for various parameters, such as the length of the varying bottom, depth ratio, angle of incidence, and flexural rigidity. It is observed that moderate values of flexural rigidity and depth ratio significantly contribute to an optimum reflection coefficient and reduce the wave force on the wall and breakwater. Remarkably, the outcomes of this study are assumed to be applicable in the construction of this type of breakwater in coastal regions.


Behera H, Kaligatla RB, Sahoo T (2015) Wave trapping by porous barrier in the presence of step type bottom. Wave Motion 57:219-230. https://doi.org/10.1016/j.wavemoti.2015.04.005
Berkhoff JCW (1973) Computation of combined refraction diffraction. In Proceedings of 13th International Conference on Coastal Engineering, Vancouver, Canada, ASCE, 471-490. https://doi.org/10.1061/9780872620490.027
Chamberlain PG, Porter D (1995) The modified mild-slope equation. Journal of Fluid Mechanics 291:393-407. https://doi.org/10.1017/S0022112095002758
Chwang AT (1983) A porous-wavemaker theory. Journal of Fluid Mechanics 132:395-406. https://doi.org/10.1017/S0022112083001676
Dalrymple RA, Kirby JT (1986) Water waves over ripples. Journal of Waterway, Port, Coastal, and Ocean Engineering 112(2):309-319.
Das S, Bora SN (2018) Oblique water wave damping by two submerged thin vertical porous plates of different heights. Computational and Applied Mathematics 37(3):3759-3779. https://link.springer.com/article/10.1007/s40314-017-0545-7
Gayen R, Mondal A (2014) A hypersingular integral equation approach to the porous plate problem. Applied Ocean Research 46:70-78. https://doi.org/10.1016/j.apor.2014.01.006
Gupta S, Naskar T, Gayen R (2022) Scattering of water waves by dual asymmetric vertical flexible porous plates. Waves in Random and Complex Media, 1-25. https://doi.org/10.1080/17455030.2021.2022247
Kaligatla RB, Koley S, Sahoo T (2015) Trapping of surface gravity waves by a vertical flexible porous plate near a wall. Journal of Applied Mathematics and Physics 66(5):2677-2702. https://link.springer.com/article/10.1007/s00033-015-0521-2
Kaligatla RB, Manisha, Sahoo T (2017) Wave trapping by dual porous barriers near a wall in the presence of bottom undulation. Journal of Marine Science and Application 16:286-297. http://html.rhhz.net/jmsa/html/20170304.html
Kaligatla RB, Tabssum S, Sahoo T (2018) Effect of bottom topography on wave scattering by multiple porous barriers. Meccanica 53(4):887-903. https://link.springer.com/article/10.1007/s11012-017-0790-2
Koley S, Kaligatla RB, Sahoo T (2015) Oblique wave scattering by a vertical flexible porous plate. Studies in Applied Mathematics 135(1):1-34. https://onlinelibrary.wiley.com/doi/full/10.1111/sapm. 12076
Krishna KA, Karaseeri AG, Karmakar D (2023) Oblique wave propagation through composite permeable porous structures. Marine Systems and Ocean Technology 17(3-4):164-187. https://link.springer.com/article/10.1007/s40868-022-00122-1
Krishnendu P, Balaji R (2020) Hydrodynamic performance analysis of an integrated wave energy absorption system. Ocean Engineering 195:106499. https://doi.org/10.1016/j.oceaneng.2019.106499
Lee MM, Chwang AT (2000) Scattering and radiation of water waves by permeable barriers. Physics of Fluids 12:54-65. https://doi.org/10.1063/1.870284
Li Y, Liu Y, Teng B (2006) Porous effect parameter of thin permeable plates. Coastal Engineering Journal 48(4):309-336. https://doi.org/10.1142/S0578563406001441
Liu Y, Li Y, Teng B (2007) Wave interaction with a new type perforated breakwater. Acta Mechanica Sinica 23(4):351-358. https://link.springer.com/article/10.1007/s10409-007-0086-1
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
Porter D, Staziker DJ (1995) Extensions of the mild-slope equation. Journal of Fluid Mechanics 300:367-382. https://doi.org/10.1017/S0022112095003727
Sahoo T (1998) On the scattering of water waves by porous barriers. Journal of Applied Mathematics and Mechanics 78:364-370. https://doi.org/10.1002/(SICI)1521-4001(199805)78:5
Sahoo T, Lee MM, Chwang AT (2000) Trapping and generation of waves by vertical porous structures. Journal of Engineering Mechanics 126:1074-1082. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:10(1074)
Suh KD, Park WS (1995) Wave reflection from perforated wall caisson breakwaters. Coastal Engineering 26(3-4):177-193. https://doi.org/10.1016/0378-3839(95)00027-5
Tabssum S, Kaligatla RB, Sahoo T (2020) Surface gravity wave interaction with a partial porous breakwater in the presence of bottom undulation. Journal of Engineering Mechanics 146(9):04020088. https://doi.org/10.1061/(ASCE) EM.1943-7889.0001818
Venkateswarlu V, Karmakar D (2020) Significance of seabed characteristics on wave transformation in the presence of stratified porous block. Coastal Engineering Journal, 62(1):1-22. https://doi.org/10.1080/21664250.2019.1676366
Williams AN, Wang KH (2003) Flexible porous wave barrier for enhanced wetlands habitat restoration. Journal of Engineering Mechanics 129:1-8. https://ascelibrary.org/doi/abs/10.1061/(ASCE) 0733-9399(2003)129:1(1)
Yip TL, Sahoo T, Chwang AT (2002) Trapping of surface waves by porous and flexible structures. Wave Motion 35(1):41-54. https://doi.org/10.1016/S0165-2125(01)00074-9


Received date: 2023-03-15;Accepted date: 2023-06-25。
Corresponding author: Saista Tabssum,E-mail:zebaxavier@gmail.com
Last Update: 2024-05-28