Oblique Wave Diffraction by Parallel Thin Vertical Barriers with Gaps
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 4
Abstract
The problem of oblique water wave diffraction by two equal thin, parallel, fixed vertical barriers with gaps present in uniform finite-depth water is investigated here. Three types of barrier configurations are considered. A one-term Galerkin approximation is used to evaluate upper and lower bounds for reflection and transmission coefficients for each configuration. These bounds are seen to be very close numerically for all wave numbers and as such their averages produce good numerical estimates for these coefficients. Only the bounds for the reflection coefficient are numerically computed. These are also numerically compared with the results obtained by using multiterm Galerkin approximations involving Chebyshev polynomials for a wide range of parameters. Numerical results for the reflection coefficients for the three barrier configurations are presented graphically. It is seen that total reflection occurs only for the surface-piercing barriers while total transmission occurs for all the three configurations considered here. It is also observed that the introduction of an equal second barrier to a submerged barrier increases the reflection coefficient considerably in some frequency bands and as such submerged double barrier configurations are preferable to a submerged single barrier for the purpose of reflecting more wave energy into the open sea.
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References
1.
Banerjea, S., and Mandal, B. N.(1993). “Solution of a singular integral equation in a double interval arising in the theory of water waves.”Appl. Math. Lett., 6(3), 81–84.
2.
Evans, D. V.(1970). “Diffraction of water waves by submerged vertical plate.”J. Fluid Mech., Cambridge, U.K., 40, 433–451.
3.
Evans, D. V.(1975). “A note on the total reflection or transmission of surface waves in the presence of parallel obstacles.”J. Fluid Mech., Cambridge, U.K., 67, 465–472.
4.
Evans, D. V., and Morris, C. A. N.(1972a). “The effect of a fixed vertical barrier on oblique incident surface waves in deep water.”J. Inst. Math. Applications, 9(2), 198–204.
5.
Evans, D. V., and Morris, C. A. N.(1972b). “Complementary approximations to the solution of a problem in water waves.”J. Inst. Math. Applications, 10(1), 1–9.
6.
Jarvis, R. J.(1971). “The scattering of surface waves by two vertical plane barriers.”J. Inst. Math. Applications, 7(2), 207–215.
7.
Levine, H., and Rodemich, E. (1958). “Scattering of surface waves on an ideal fluid.”Tech. Rep. No. 78, Math. and Statistics Lab., Stanford Univ., Stanford, Calif.
8.
Mandal, B. N., and Dolai, D. P.(1994). “Oblique water wave diffraction by thin vertical barriers in water or uniform finite depth.”Appl. Oc. Res., 16(4), 195–203.
9.
Mandal, B. N., and Kundu, P. K.(1990). “A note on scattering of water waves by a submerged nearly vertical plate.”SIAM J. Appl. Math., 50(5), 1221–1231.
10.
McIver, P.(1985). “Scattering of surface waves by two surface piercing vertical barriers.”IMA J. Appl. Math., 35(1), 1–17.
11.
Morris, C. A. N.(1975). “A variational approach to an unsymmetric water wave scattering problem.”J. Engrg. Math., 9(3), 291–300.
12.
Newman, J. N.(1974). “Interaction of water waves with two closely spaced vertical obstacles.”J. Fluid Mech., Cambridge, U.K., 66, 97–106.
13.
Packham, B. A., and Williams, W. E.(1972). “A note on the transmission of water waves through small apertures.”J. Inst. Math. Applications, 10(2), 176–184.
14.
Porter, R., and Evans, D. V.(1995). “Complementary approximations to wave scattering by vertical barriers.”J. Fluid Mech., Cambridge, U.K., 294, 155–180.
15.
Ursell, F.(1947). “The effect of a fixed vertical barrier on surface waves in deep water.”Proc., Cambridge Phil. Soc., 43, 374–382.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Jul 1, 1997
Published in print: Jul 1997
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