Surface Gravity Wave Interaction with a Partial Porous Breakwater in the Presence of Bottom Undulation
Publication: Journal of Engineering Mechanics
Volume 146, Issue 9
Abstract
Using potential flow theory, oblique wave scattering and trapping by a partial porous breakwater having finite width are studied under the assumption of small-amplitude water wave theory in the presence of seabed undulation. This study is performed for regular incident waves that approach from deeper water depth and impinge on the porous breakwater at lower water depth. The two constant levels of deeper and lower bottoms are linked by a smooth arbitrary bottom topography, which may be regarded as a continental slope. In the lower-depth water, two types of porous breakwaters, namely, bottom-standing and surface-piercing breakwaters, are considered with and without a seawall. The analytical method of eigenfunction expansion is adopted for constant water depth, whereas an approximate method of the modified mild-slope equation is employed for varying water depth. Different bottom configurations are applied in this study. Reflection and transmission coefficients of waves and wave force on seawall are calculated for various physical parameters related to porous breakwater and waves. The role of seabed undulation on wave scattering and trapping is analyzed. The effectiveness of the breakwater is studied from the reflection and transmission coefficients. Results show a major difference in breakwater’s performance in scattering and dissipating waves under the condition of varying water depth compared to the case of constant depth of water. The tranquillity zone is obtained by optimizing various physical parameters. This study provides some theoretical knowledge related to wave interaction with partial porous structures under varying water-depth conditions. Moreover, it finds engineering applications concerned with the creation of tranquility regions and the protection of seawall.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
RBK acknowledges the funding support provided by Science and Engineering Research Board (India) under ECRA with Grant No. ECR/2017/001859. TS acknowledges the partial support received from the Department of Science and Technology, Government of India through Award No. DST/CCP/CoE/79/2017(G).
References
Behera, H., R. B. Kaligatla, and T. Sahoo. 2015. “Wave trapping by porous barrier in the presence of step type bottom.” Wave Motion 57 (S5ep): 219–230. https://doi.org/10.1016/j.wavemoti.2015.04.005.
Behera, H., and C.-O. Ng. 2018. “Interaction between oblique waves and multiple bottom-standing flexible porous barriers near a rigid wall.” Meccanica 53 (4–5): 871–885. https://doi.org/10.1007/s11012-017-0789-8.
Chamberlain, P. G., and D. Porter. 1996. “Approximations to wave trapping by topography.” J. Fluid Mech. 325 (Oct): 357–376. https://doi.org/10.1017/S0022112096008154.
Dalrymple, R. A., and J. T. Kirby. 1986. “Water waves over ripples.” J. Waterway, Port, Coastal, Ocean Eng. 112 (2): 309–319. https://doi.org/10.1061/(ASCE)0733-950X(1986)112:2(309).
Dalrymple, R. A., M. A. Losada, and P. A. Martin. 1991. “Reflection and transmission from porous structures under oblique wave attack.” J. Fluid Mech. 224 (Mar): 625–644. https://doi.org/10.1017/S0022112091001908.
Das, S., and S. N. Bora. 2014. “Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom.” Appl. Ocean Res. 47 (May): 373–385. https://doi.org/10.1016/j.apor.2014.07.001.
Dattatri, J., H. Raman, and N. J. Shankar. 1978. “Performance characteristics of submerged breakwaters.” In Proc., 16th Int. Conf. on Coastal Engineering, Hamburg, 2153–2171. Reston, VA: ASCE.
Izzat Na’im, I., A. R. M. Shahrizal, and M. D. Safari. 2018. “A short review of submerged breakwaters.” In Proc., MATEC Web of Conf., 17. Red Hook, NY: Curran Associates. https://doi.org/10.1051/matecconf/201820301005.
Kaligatla, R. B., M. Sharma, and T. Sahoo. 2017. “Wave trapping by dual porous barriers near a wall in the presence of bottom undulation.” J. Mar. Sci. Appl. 16 (3): 286–297. https://doi.org/10.1007/s11804-017-1423-9.
Kaligatla, R. B., S. Tabssum, and T. Sahoo. 2018. “Effect of bottom topography on wave scattering by multiple porous barriers.” Meccanica 53 (4–5): 887–903. https://doi.org/10.1007/s11012-017-0790-2.
Koley, S., H. Behera, and T. Sahoo. 2014. “Oblique wave trapping by porous structures near a wall.” J. Eng. Mech. 141 (3): 04014122. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000843.
Koley, S., A. Sarkar, and T. Sahoo. 2015. “Interaction of gravity waves with bottom-standing submerged structures having perforated outer-layer placed on a sloping bed.” Appl. Ocean Res. 52 (Aug): 245–260. https://doi.org/10.1016/j.apor.2015.06.003.
Losada, I. J., R. Silva, and M. A. Losada. 1996. “3-D non-breaking regular wave interaction with submerged breakwaters.” Coastal Eng. 28 (1–4): 229–248. https://doi.org/10.1016/0378-3839(96)00019-1.
Madsen, P. A. 1983. “Wave reflection from a vertical permeable wave absorber.” Coastal Eng. 7 (4): 381–396. https://doi.org/10.1016/0378-3839(83)90005-4.
Mallayachari, V., and V. Sundar. 1994. “Reflection characteristics of permeable seawalls.” Coastal Eng. 23 (1–2): 135–150. https://doi.org/10.1016/0378-3839(94)90019-1.
Porter, D., and D. J. Staziker. 1995. “Extensions of the mild-slope equation.” J. Fluid Mech. 300 (Oct): 367–382. https://doi.org/10.1017/S0022112095003727.
Porter, R., and D. Porter. 2000. “Water wave scattering by a step of arbitrary profile.” J. Fluid Mech. 411 (May): 131–164. https://doi.org/10.1017/S0022112099008101.
Rojanakamthorn, S., M. Isobe, and A. Watanabe. 1990. “Modeling of wave transformation on submerged breakwater.” In Proc., 22nd Coastal Engineering Conf., Delft., 1060–1073. Reston, VA: ASCE.
Sharma, M., R. B. Kaligatla, and T. Sahoo. 2019. “Effect of bottom undulation for mitigating wave-induced forces on a floating bridge.” Wave Motion 89 (Jun): 166–184. https://doi.org/10.1016/j.wavemoti.2019.03.007.
Sharma, M., R. B. Kaligatla, and T. Sahoo. 2020. “Wave interaction with a submerged floating tunnel in the presence of a bottom mounted submerged porous breakwater.” Appl. Ocean Res. 96 (Mar): 102069. https://doi.org/10.1016/j.apor.2020.102069.
Sollitt, C. K., and R. H. Cross. 1972. “Wave transmission through permeable breakwaters.” Proc. 13th Coastal Eng. Conf., 1827–1846. Reston, VA: ASCE.
Suh, K. D., C. Lee, Y. H. Park, and T. H. Lee. 2001. “Experimental verification of horizontal two-dimensional modified mild-slope equation model.” Coastal Eng. 44 (1): 1–12. https://doi.org/10.1016/S0378-3839(01)00018-7.
Tabssum, S., R. B. Kaligatla, and T. Sahoo. 2020. “Gravity wave interaction with a porous breakwater in a two-layer ocean of varying depth.” Ocean Eng. 196 (Jan): 106816. https://doi.org/10.1016/j.oceaneng.2019.106816.
Zhao, Y., H. J. Li, and Y. Liu. 2017. “Oblique wave scattering by a submerged porous breakwater with a partially reflecting sidewall.” J. Mar. Sci. Tech. 25 (4): 383–392.
Zhu, S. 2001. “Water waves within a porous medium on an undulating bed.” Coastal Eng. 42 (1): 87–101. https://doi.org/10.1016/S0378-3839(00)00050-8.
Zhu, S., and A. T. Chwang. 2001. “Analytical study of porous wave absorber.” J. Eng. Mech. 127 (4): 326–332. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(326).
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 9 • September 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Aug 20, 2019
Accepted: Mar 16, 2020
Published online: Jun 18, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 18, 2020
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