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Some effects of surface tension on steep water waves. Part 2

Published online by Cambridge University Press:  19 April 2006

S. J. Hogan
S. J. Hogan
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
Present address: Applied Mathematics Department 101-50, California Institute of Technology, Pasadena, California 91125.
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Abstract

This paper continues an investigation of the effects of surface tension on steep water waves in deep water begun in Hogan (1979a). A Stokes-type expansion method is given which can be applied to most wavelengths. For capillary waves (2 cm or less) it is found that the surface of the highest wave encloses a bubble of air, as was found for pure capillary waves by Crapper (1957). For intermediate waves (20 cm) the wave profiles are similar to those of pure gravity waves and the wave properties increase monotonically. For gravity waves (200 cm) the wave properties all exhibit a maximum just short of the maximum wave height obtained by the method. The integral properties for all the waves are drawn and given in numerical form in the appendix.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 3 , 13 February 1980 , pp. 417 - 445
Copyright
© 1980 Cambridge University Press

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References

Cokelet, E. D. 1977 Phil. Trans. Roy. Soc. A 286, 183–230.
Crapper, G. D. 1957 J. Fluid Mech. 2, 532–540.
Crapper, G. D. 1979 J. Fluid Mech. 94, 13–24.
Hogan, S. J. 1979a J. Fluid Mech. 91, 167–180.
Hogan, S. J. 1979b Ph.D. Dissertation, Cambridge University.
Longuet-Higgins, M. S. 1975 Proc. Roy. Soc. A342, 157–174.
Longuet-Higgins, M. S. 1978a Proc. Roy. Soc. A 360, 471–488.
Longuet-Higgins, M. S. 1978b Proc. Roy. Soc. A 360, 489–506.
Longuet-Higgins, M. S. & Fox, M. J. H. 1977 J. Fluid Mech. 80, 721–742.
Longuet-Higgins, M. S. & Fox, M. J. H. 1978 J. Fluid Mech. 85, 769–786.
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Deep-Sea Res. 11, 529–562.
Schwartz, L. W. 1972 Ph.D. Dissertation, Stanford University.
Schwartz, L. W. 1974 J. Fluid Mech. 62, 553–578.
Stokes, G. G. 1880 Math. & Phys. Papers 1, 225–228.
Wehausen, J. V. & Laitone, E. V. 1960 Encyclopaedia of Physics (ed. S. Flügge), vol. 9, pp. 446–778.
Wilton, J. R. 1915 Phil. Mag. 29 (6), 688–700.