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The singularity at the crest of a finite amplitude progressive Stokes wave

Published online by Cambridge University Press:  29 March 2006

Malcolm A. Grant
Malcolm A. Grant
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology
Present address: Mathematics Department, University of Oslo.
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Abstract

Expansions have been given in the past for steady Stokes waves at or near a largest wave with a 120° corner. It is shown here that the solution is more complicated than has been assumed: that the corner is not a regular singular point, and that waves of less than maximum amplitude have singularities of a different order.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 2 , 19 June 1973 , pp. 257 - 262
Copyright
© 1973 Cambridge University Press

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References

Havelock, T. H. 1919 Periodic irrotational waves of finite height. Proc. Roy. Soc A 95, 38–51.Google Scholar
Krasovskii, Yu. P. 1962 On the theory of steady-state waves of finite amplitude U.S.S.R. Comp. Math. & Math. Phys. 1, 996–1018.Google Scholar
Longuet-Higgins, M. S. 1973 On the form of the highest progressive and standing waves in deep water. Proc. Roy. Soc. A 331, 445.Google Scholar
Michell, J. H. 1893 The highest waves in water. Phil. Mag. 36 (5), 430–437.Google Scholar
Nekrasov, A. I. 1920 On Stokes’ wave. Isv. Ivanovo-Voznesesk. Politekhn. Inst. pp. 81–89.Google Scholar
Schwartz, L. W. 1972 Analytic continuation of Stokes’ expansion for gravity waves. Ph.D. thesis, Stanford University.
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik, vol. 4, pp. 446–758. Springer.
Yamada, H. 1957 Highest waves of permanent type on the surface of deep water. Appl. Mech. Res. Rep., Kyushu Univ. 5 (18), 37–52.Google Scholar