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The behaviour near the crest of an extreme Stokes wave

Published online by Cambridge University Press:  25 February 2010

L. E. FRAENKEL*
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK email: L.E.Fraenkel@bath.ac.uk

Abstract

In the preceding paper by Fraenkel & Harwin, the existence theorem leaves a gap in the description of the extreme wave that is constructed there. The form of the wave in a neighbourhood of the crest is not described accurately enough. This weakness is repaired in the present paper.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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References

[1]Amick, C.J. & Fraenkel, L.E. (1987) On the behavior near the crest of waves of extreme form. Trans. Amer. Math. Soc. 299, 273298.CrossRefGoogle Scholar
[2]Fraenkel, L.E. & Harwin, P.J. (2010) On the local uniqueness and the profile of the extreme Stokes wave. Euro. Jnl of Appl. Math. 21, 137163.CrossRefGoogle Scholar
[3]Grant, M.A. (1973) The singularity at the crest of a finite amplitude progressive Stokes wave. J. Fluid Mech. 59, 257262.CrossRefGoogle Scholar
[4]Longuet-Higgins, M.S. & Fox, M.J.H. (1977) Theory of the almost-highest wave: the inner solution. J. Fluid Mech. 80, 721741.CrossRefGoogle Scholar
[5]McLeod, J.B. (1987) The asymptotic behavior near the crest of waves of extreme form. Trans. Amer. Math. Soc. 299, 299302.CrossRefGoogle Scholar
[6]Titchmarsh, E.C. (1948) Introduction to the theory of Fourier integrals, 2nd edn.Oxford: Clarendon Press.Google Scholar