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An integral equation for unsteady surface waves and a comment on the Boussinesq equation

Published online by Cambridge University Press:  29 March 2006

J. G. B. Byatt-Smith
J. G. B. Byatt-Smith
Affiliation:
University of California Aeronautical Sciences Division, Berkeley, California 94720 Present address: Trait Institute of Mathematical Physics, University of Edinburgh, Edinburgh, Scotland
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Abstract

An integral equation for unsteady inviscid surface waves has been obtained. Existing known approximations are all derived from the one equation. The Boussinesq equation is obtained and criticized.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 4 , 29 October 1971 , pp. 625 - 633
Copyright
© 1971 Cambridge University Press

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References

Atry, G. B. 1845 Tides and Waves. London: Enoyclopaedia Metropolitana.
Benny, D. J. & Luke, S. C. 1964 J. Math. & Phys. 43, 4.
Boussinesq, J. 1872 J. Math. Pure Appl. 2, 17, 55–108.
Camfield, F. E. & Street, R. L. 1969 A.S.Ch.E. J. Waterways and Harbours Div. no. 95.
Chan, R. K. C., Street, R. L. & Strelkoff, T. 1969 Dept. Civil Eng., Stanford Univ. Tech. Rept. no. 104.
Korteweg, D. J. & de Vries, G. 1895 Phil. Mag. (5) 38, 422–43.
Laitone, E. V. 1960 J. Fluid Mech. 9, 430–444.
Lax, P. 1968 Comm. Pure & Appl. Math. 21, 467–490.
Lighthill, M. J. 1958 Generalized functions. Cambridge University Press.
Mayer, R. E. 1962 Brown Univ. Tech. Rept.
Peregrine, P. H. 1966 J. Fluid Mech. 25, 321–330.
Russell, S. 1844 Rept. Brit. Assn. p. 311.
Stokes, G. G. 1849 Trans. Camb. Phil. Soc. 8, 441.
Whitham, G. B. 1965a Proc. Roy. Soc. A 283, 238–261.
Whitham, G. B. 1965b J. Fluid Mech. 22, 273–283.
Whitham, G. B. 1967 Proc. Roy. Soc. A 299, 6–25.
Woods, L. C. 1961 The Theory of Subsonic Plane Flow. Cambridge University Press.