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Mclver, P., Water-wave diffraction by thin porous breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(2), pp. 66–70, 1999. [Crossref]
8.
Evans, D.V. & Peter, M.A., Asymptotic reflection of linear water waves by submerged horizontal porous plates. Journal of Engineering Mathematics, 69(2–3), pp. 135–154, 2011.
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Tsai, C. & Young, D., The method of fundamental solutions for water-wave diffraction by thin porous breakwater. Journal of Mechanics, 27(01), pp. 149–155, 2011. [Crossref]
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Gayen, R. & Mondal, A., A hypersingular integral equation approach to the porous plate problem. Applied Ocean Research, 46, pp. 70–78, 2014. [Crossref]
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Open Access
Research article

Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean

dibakar mondal1,
sudeshna banerjea2
1
Department of Mathematics, Government General Degree College at Kalna-I, Muragacha, Medgachi, Burdwan - 713405, India
2
Department of Mathematics, Jadavpur University, Kolkata-700032, India
International Journal of Computational Methods and Experimental Measurements
|
Volume 4, Issue 4, 2016
|
Pages 532-542
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

In this paper, we study the problem of scattering of surface water waves by a thin circular arc shaped porous plate submerged in the deep ocean. The problem is formulated in terms of a hypersingular integral equation of the second kind in terms of an unknown function representing the difference of potential function across the curved barrier. The hypersingular integral equation is then solved by a collocation method after expanding the unknown function in terms of Chebyshev polynomials of the second kind. Using the solution of the hyper-singular integral equation, the reflection coefficient, trans- mission coefficient and energy dissipation coefficient are computed and depicted graphically against the wave number. Known results for the rigid curved barrier are recovered. It is observed that the poros- ity of the barrier reduces the reflection and transmission of the waves and enhances the dissipation of wave energy. The reflection coefficient and dissipation of wave energy decreases as the length of the porous curved barrier increases. Also the reflection coefficient is almost independent of the inertial force coefficient of the material of the porous barrier. However, the inertial force coefficient of the material of the porous barrier enhances transmission and reduces dissipation of wave energy.

Keywords: Curved porous plate, Dissipation of wave energy, Reflection coefficient, Transmission coefficient, Water wave scattering

1. Introduction

2. Formulation of the Problem

3. Method of Solution

4. Numerical Results

5. Conclusion

Acknowledgments

This work is supported by UGC through UPE 2 at Jadavpur University and CSIR (No 25/0253/16/EMRII).

References
1.
Dean, W., On the reflexion of surface waves by a submerged plane barrier. Mathemati- cal Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 41, pp. 231–238, 1945.
2.
Ursell, F., The effect of a fixed vertical barrier on surface waves in deep water. Math- ematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 43, pp. 374–382, 1947.
3.
Evans, D., Diffraction of water waves by a submerged vertical plate. Journal of Fluid Mechamos, 40(03), pp. 433–451, 1970. [Crossref]
4.
Chwang, A.T., A porous-wavemaker theory. Journal of Fluid Mechanics, 132,
5.
Sollitt, C.K. & Cross, R.H., Wave transmission through permeable breakwaters. Coastal Engineering Proceedings, 1(13), 1972.
6.
Yu, X., Diffraction of water waves by porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 121(6), pp. 275–282, 1995. [Crossref]
7.
Mclver, P., Water-wave diffraction by thin porous breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(2), pp. 66–70, 1999. [Crossref]
8.
Evans, D.V. & Peter, M.A., Asymptotic reflection of linear water waves by submerged horizontal porous plates. Journal of Engineering Mathematics, 69(2–3), pp. 135–154, 2011.
9.
Tsai, C. & Young, D., The method of fundamental solutions for water-wave diffraction by thin porous breakwater. Journal of Mechanics, 27(01), pp. 149–155, 2011. [Crossref]
10.
Gayen, R. & Mondal, A., A hypersingular integral equation approach to the porous plate problem. Applied Ocean Research, 46, pp. 70–78, 2014. [Crossref]
11.
Parsons, N. & Martin, P., Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Applied Ocean Research, 16(3), pp. 129–139, 1994. [Crossref]
12.
Yu, X. & Chwang, A.T., Wave-induced oscillation in harbor with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 120(2), pp. 125–144, 1994. [Crossref]
Cite this:
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Mondal, D. & Banerjea, S. (2016). Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean. Int. J. Comput. Methods Exp. Meas., 4(4), 532-542. https://doi.org/10.2495/CMEM-V4-N4-532-542
D. Mondal and S. Banerjea, "Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean," Int. J. Comput. Methods Exp. Meas., vol. 4, no. 4, pp. 532-542, 2016. https://doi.org/10.2495/CMEM-V4-N4-532-542
@research-article{Mondal2016ScatteringOW,
title={Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean},
author={Dibakar Mondal and Sudeshna Banerjea},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2016},
page={532-542},
doi={https://doi.org/10.2495/CMEM-V4-N4-532-542}
}
Dibakar Mondal, et al. "Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean." International Journal of Computational Methods and Experimental Measurements, v 4, pp 532-542. doi: https://doi.org/10.2495/CMEM-V4-N4-532-542
Dibakar Mondal and Sudeshna Banerjea. "Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean." International Journal of Computational Methods and Experimental Measurements, 4, (2016): 532-542. doi: https://doi.org/10.2495/CMEM-V4-N4-532-542
MONDAL D， BANERJEA S. Scattering of Water Waves by a Porous Circular Arc-Shaped Barrier Submerged in Ocean[J]. International Journal of Computational Methods and Experimental Measurements， 2016， 4(4)： 532-542. https://doi.org/10.2495/CMEM-V4-N4-532-542