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A note on the uniqueness of small-amplitude water waves travelling in a region of varying depth

Published online by Cambridge University Press:  24 October 2008

G. F. Fitz-Gerald  and
R. H. J. Grimshaw
G. F. Fitz-Gerald
Affiliation:
Department of Mathematics and Computer Science, Royal Melbourne Institute of Technology, Melbourne, Victoria, 3000, Australia
R. H. J. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria, 3052, Australia
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Extract

The two-dimensional, irrotational, linear theory used in the investigation of the propagation of monochromatic surface gravity waves in a region of varying depth is considered. Uniqueness of the velocity potential is established for bottom profiles satisfying certain convexity conditions. These include the majority of profiles of physical interest.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 3 , November 1979 , pp. 511 - 519
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Fitz-Gerald, G. F.Phil. Trans. Roy. Soc. 284 (1976), 49–89.Google Scholar
(2)Gradshteyn, I. S. and Ryzhik, I. M.Tables of integrals, series and products (New York, Academic Press, 1965).Google Scholar
(3)Hamilton, J.J. Fluid Mech. 83 (1977), 289–310.CrossRefGoogle Scholar
(4)Kreisel, G.Quart. Appl. Maths. 7 (1949), 21–44.Google Scholar
(5)Wehausen, J. V. and Laitone, E. V.Surface waves. Handbuch der Phusik 9 (1960) 446–778Google Scholar