Trapping and Generation of Waves by Vertical Porous Structures
Publication: Journal of Engineering Mechanics
Volume 126, Issue 10
Abstract
The trapping and generation of surface waves by submerged vertical permeable barriers or plates kept at one end of a semi-infinitely long channel of finite depth are investigated for various barrier and plate configurations. The various fixed barrier configurations are (1) a surface-piercing barrier; (2) a bottom-touching barrier; (3) a barrier with a gap; and (4) a fully submerged barrier. The different moving plate (or wavemaker) configurations are of types 1, 2, and 4, respectively. The boundary value problems are converted to dual/triple series relations by a suitable application of the eigenfunction expansion method and then the full solutions are obtained by the least-squares method. The variations of reflection coefficients are obtained and discussed for different values of the porous-effect parameter, the normalized distance between the barrier and the channel end-wall, and the length of submergence of barriers for all types of barrier configurations. The dynamic pressure distributions for various porous-effect parameters are analyzed for the three types of wavemakers. The wave amplitudes at large distances are obtained and analyzed for different values of the porous-effect parameter and the distance between the wavemaker and the channel end-wall.
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References
1.
Abul-Azm, A. G. (1993). “Wave diffraction through submerged breakwaters.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 119(6), 587–605.
2.
Chwang, A. T. ( 1983). “A porous wavemaker theory.” J. Fluid Mech., Cambridge, U.K., 132, 395–406.
3.
Chwang, A. T., and Chan, A. T. ( 1998). “Interaction between porous media and wave motion.” Annu. Rev. Fluid Mech., 30, 53–84.
4.
Chwang, A. T., and Dong, Z. ( 1984). “Wave trapping due to a porous plate.” Proc., 15th ONR Symp. Naval Hydrodyn., National Academy Press, Washington, D.C., 407–417.
5.
Chwang, A. T., and Li, W. ( 1983). “A piston-type porous wavemaker theory.” J. Engrg. Mathematics, 17, 301–313.
6.
Dalrymple, R. A., and Martin, P. A. (1990). “Wave diffraction through offshore breakwater.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 116(6), 712–741.
7.
Evans, D. V. ( 1976). “A note on the waves produced by small oscillations of a partially immersed vertical plate.” J. Inst. of Mathematics and Its Applications, 17, 135–140.
8.
Evans, D. V., and Kuznetsov, N. ( 1997). “Trapped modes.” Gravity waves in water of finite depth, J. N. Hunt, ed., Computational Mechanics Publication, Southampton, U.K., 127–168.
9.
Evans, D. V., and Linton, C. M. ( 1989). “Active devices for the reduction of wave intensity.” Appl. Oc. Res., Southampton, U.K., 11, 26–32.
10.
Evans, D. V., and Porter, D. ( 1996). “Hydrodynamic characteristics of a thin rolling plate in finite depth of water.” Appl. Oc. Res., Southampton, U.K., 18, 215–228.
11.
Fienerman, R. P., and Kelman, R. B. ( 1974). “The convergence of least squares approximations for dual orthogonal series.” Glasgow Math. J., Edinburgh, U.K., 15, 82–84.
12.
Franco, L. ( 1994). “Vertical breakwaters: The Italian experience.” Coast. Engrg., Amsterdam, 22, 31–55.
13.
Greenspan, H. P. ( 1970). “A note on edge waves in a stratified fluid.” Studies in Appl. Mathematics, 49(4), 381–388.
14.
Havelock, T. H. ( 1929). “Forced surface waves on water.” Philosophical Mag., London, 8, 569–576.
15.
Jones, D. S. ( 1953). “The eigenvalues of ∇2u − λu = 0 when the boundary conditions are given on semi-infinite domains.” Proc. Cambridge Philosophical Soc., Cambridge, U.K., 49, 668–684.
16.
Kelman, R. B., and Chester, A. K., Jr. ( 1973). “Least squares approximations for dual trigonometric series.” Glasgow Math. J., Edinburgh, U.K., 14, 111–119.
17.
Lamb, H. ( 1945). Hydrodynamics, Dover, New York.
18.
Leblond, P. H., and Mysak, L. A. ( 1978). Waves in the ocean, Elsevier, Amsterdam.
19.
Lee, M. M., and Chwang, A. T. ( 2000). “Scattering and radiation of water waves by permeable barriers.” Phys. of Fluids, 12, 54–65.
20.
Linton, C. M., and Evans, D. V. ( 1991). “Trapped modes above a submerged horizontal plate.” Quarterly J. Mech. and Appl. Mathematics, Oxford, U.K., 44(3), 487–506.
21.
Losada, I. J., Losada, M. A., and Roldan, A. J. ( 1992). “Propagation of oblique incident waves past rigid vertical thin barrier.” Appl. Oc. Res., Southampton, U.K., 14, 191–199.
22.
Martin, P. A., and Farina, L. ( 1997). “Radiation of water waves by a heaving submerged horizontal disk.” J. Fluid Mech., Cambridge, U.K., 337, 365–379.
23.
Parsons, N. F., and Martin, P. A. ( 1995). “Trapping of water waves by submerged plates by using hypersingular integral equations.” J. Fluid Mech., Cambridge, U.K., 284, 359–375.
24.
Stokes, G. G. ( 1846). “Report on recent researches in hydrodynamics.” Rep. to 16th Meeting of the British Assn. for the Advancement of Sci., Southampton, Murrey, London, 1–20.
25.
Ursell, F. ( 1948). “On the waves due to the rolling of a thin strip.” Quarterly J. Mech. and Appl. Mathematics, Oxford, U.K., 1, 246–252.
26.
Ursell, F. ( 1951). “Trapping modes in the theory of surface waves.” Proc. Cambridge Philosophical Soc., Cambridge, U.K., 47, 347–358.
27.
Wang, K.-H., and Ren, X. ( 1994). “An effective wave-trapping system.” Oc. Engrg., 21, 155–178.
28.
Yu, X., and Chwang, A. T. (1994). “Wave induced oscillation in harbour with porous breakwaters.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 120(2), 125–144.
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Received: Sep 7, 1999
Published online: Oct 1, 2000
Published in print: Oct 2000
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