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Theories for the diffraction of three-dimensional surface waves by plane vertical obstacles

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  26 February 2010

D. C. Shaw
D. C. Shaw
Affiliation:
Department of Mathematics, Imperial College, London. SW7 2AZ
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Attempts to extend known two-dimensional results (Ursell, 1947) to the fully three-dimensional case can lead to unpredictable results. We show how the use of a variational approximation for a finite plane vertical barrier leads to apparently different results when different formulations are used. The reason for this is not so much that the method is wrong, but rather that several different limits are taken in the process, which are hard to control. We suggest an alternative matching scheme, based on Ayad and Leppington (1977), which holds for the case ka → ∞, l/a → ∞, kl → ∞, where / is the length of the barrier, a its depth and k the wavelength of the incident wave. The method is applied to a channel with impeding side walls, as a model of French's (1977) wave-energy device.

MSC classification

Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 178 - 195
Copyright
Copyright © University College London 1984

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References

, A. Ayad and Leppington, F. G.. J. Fluid Meek, 80 (1977), 593–604.Google Scholar
Barakat, R.. J. Fluid Meek, 13 (1962), 540–556.Google Scholar
Burger, A. P.. Proc. R. Soc. Lond., A, 252 (1959), 411–417.Google Scholar
Evans, D. V. and Morris, C. A. N.. J. Inst. Math. Applies., 9 (1972), 198–204.Google Scholar
French, M. J.. J. Meek Eng. Set, 19 (1977), 90–92.Google Scholar
Karp, S. N. Y. and Russek, A.. J. Appl. Phys., 27 (1956), 886–894.Google Scholar
Keller, J. B. and Magiros, D. G.. Comm. Pure Appl. Math., 14 (1961), 457–471.Google Scholar
Levine, H.. J. Fluid Meek, 15 (1963), 241–250.CrossRefGoogle Scholar
Noble, B.. Methods based on the Wiener-Hopf technique (Pergamon, London, 1958).Google Scholar
Shaw, D. C.. Ph.D. Thesis (University of London, 1983).Google Scholar
Ursell, F.. Proe. Camb. Phil. Soc., 43 (1947), 374–382.CrossRefGoogle Scholar
Voit, S. S.. J. Appl. Math. Meek, 25 (1961), 545.CrossRefGoogle Scholar