Abstract
A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.
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References
Sollitt C. K., Cross R. H. Wave transmission through permeable breakwaters [J]. Coastal Engineering Proceedings, 1972, 1(13): 1827–1846.
Chwang A. T. A porous-wavemaker theory [J]. Journal of Fluid Mechanics, 1983, 132: 395–406.
Sahoo T., Chan A. T., Chwang A. T. Scattering of oblique surface waves by permeable barriers [J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2000, 126(4): 196–205.
Das S., Bora S. N. Wave damping by a vertical porous structure placed near and away from a rigid vertical wall [J]. Geophysical and Astrophysical Fluid Dynamics, 2014, 108(2): 147–167.
Zhao Y., Liu Y., Li H. J. Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar [J]. Journal of Ocean University of China, 2016, 15(4): 619–626.
Zhang J., Li Q., Ding C. et al. Experimental investigation of wave-driven pore-water pressure and wave attenuation in a sandy seabed [J]. Advances in Mechanical Engineering, 2016, 8(6): 1–10.
Zhai Y., Zhang J., Jiang L. et al. Experimental study of wave motion and pore pressure around a submerged impermeable breakwater in a sandy seabed [J]. International Journal of Offshore and Polar Engineering, 2016, 28(1): 87–95.
Jeng D. S. Wave dispersion equation in a porous seabed [J]. Ocean Engineering, 2001, 28(12): 1585–1599.
Metallinos A. S., Repousis E. G., Memos C. D. Wave propagation over a submerged porous breakwater with steep slopes [J]. Ocean Engineering, 2016, 111: 424–438.
Mohapatra S. The interaction of oblique flexural gravity incident waves with a small bottom deformation on a porous ocean-bed: Green’s function approach [J]. Journal of Marine Science and Application, 2016, 15(2): 112–122.
Das S., Behera H., Sahoo T. Flexural gravity wave motion over poroelastic bed [J]. Wave Motion, 2016, 63: 135–148.
Shoushtari S. M. H. J., Cartwright N. Modelling the effects of porous media deformation on the propagation of water-table waves in a sandy unconfined aquifer [J]. Hydrogeology Journal, 2017, 25(2): 287–295.
Ye J. H., Jeng D. S. Response of porous seabed to nature loadings: Waves and currents [J]. Journal of Engineering Mechanics, 2011, 138(6): 601–613.
Zhang Y., Jeng D. S., Gao F. P. et al. An analytical solution for response of a porous seabed to combined wave and current loading [J]. Ocean Engineering, 2013, 57: 240–247.
Zhang X., Zhang G., Xu C. Stability analysis on a porous seabed under wave and current loading [J]. Marine Georesources and Geotechnology, 2017, 35(5): 710–718.
Seymour B. R., Jeng D. S., Hsu J. R. C. Transient soil response in a porous seabed with variable permeability [J]. Ocean Engineering, 1996, 23(1): 27–46.
Jeng D. S., Seymour B. R. Response in seabed of finite depth with variable permeability [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123(10): 902–911.
Zhang L. L., Cheng Y., Li J. H. et al. Wave-induced oscillatory response in a randomly heterogeneous porous seabed [J]. Ocean Engineering, 2016, 111: 116–127.
Meng Q. R., Lu D. Q. Scattering of gravity waves by a porous rectangular barrier on a seabed [J]. Journal of Hydrodynamics, 2016, 28(3): 519–522.
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The authors would like to thank Professor S. Q. Dai of Shanghai University for his helpful suggestions and thank the anonymous reviewers for their constructive comments.
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Project supported by the Ministry of Industry and Information Technology (MIIT) with the Research Project in the Fields of High-Technology Ships (Grant Nos. [2016]22, [2016]548), the National Natural Science Foundation of China (Grant No. 11472166) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20130109).
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Lin, Q., Meng, Qr. & Lu, Dq. Waves propagating over a two-layer porous barrier on a seabed. J Hydrodyn 30, 453–462 (2018). https://doi.org/10.1007/s42241-018-0041-6
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DOI: https://doi.org/10.1007/s42241-018-0041-6