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Shallow water waves on shear flows

Published online by Cambridge University Press:  29 March 2006

N. C. Freeman  and
R. S. Johnson
N. C. Freeman
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
R. S. Johnson
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
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Abstract

An equation for waves on the surface of a flow with shear is deduced and shown to reduce by suitable scaling to the classical equation of Korteweg & de Vries, which describes such motions on a stationary flow. For steady flows the corresponding theory of cnoidal waves is obtained and the results of Benjamin (1962) for a solitary wave recovered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 2 , 22 June 1970 , pp. 401 - 409
Copyright
© 1970 Cambridge University Press

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References

Benjamin, T. B. 1962 J. Fluid Mech. 12, 97–116.
Burns, J. C. 1953 Proc. Camb. Phil. Soc. 49, 695–706.
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Waltham, Mass.: Blaisdell.
Korteweg, D. J. & de Vries, G. 1895 Phil. Mag. (5) 39, 422–443.
Lamb, H. 1953 Hydrodynamics (6th ed.) Cambridge University Press.
Zabusky, N. J. 1967 In Non-linear Partial Differential Equations; Symposium on Methods of Solution (ed. W. F. Ames), 223–258. New York: Academic.