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Energy and momentum integrals for progressive capillary-gravity waves

Published online by Cambridge University Press:  19 April 2006

G. D. Crapper
G. D. Crapper
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Liverpool, P.O. Box 147, Liverpool L69 3BX
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Abstract

Definitions of energy density, energy flux and momentum flux for capillary—gravity waves are derived by integration of the equations of motion and also by Whitham's averaged Lagrangian method. We then confirm recent results due to Hogan (1979) both in the general case and in the case of pure capillary waves. Comparison with the Lagrangian results also allows us to give general definitions of ‘wave action density’ and ‘wave action flux’.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 1 , 11 September 1979 , pp. 13 - 24
Copyright
© 1979 Cambridge University Press

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References

Cokelet, E. D. 1977 Phil. Trans. Roy. Soc. A 286, 183.
Crapper, G. D. 1957 J. Fluid Mech. 2, 532.
Hasselmann, K. 1971 J. Fluid Mech. 50, 189.
Hogan, S. J. 1979 J. Fluid Mech. 91, 167.
Lighthill, M. J. 1965 J.I.M.A. 1, 269.
Longuet-Higgins, M. S. 1975 Proc. Roy. Soc. A 342, 157.
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Deep-Sea Res. 11, 529.
Luke, J. C. 1967 J. Fluid Mech. 27, 395.
Peregrine, D. H. 1976 Adv. Appl. Mech. 16, 9.
Peregrine, D. H. & Thomas, G. P. 1979 Submitted to Phil. Trans. Roy. Soc.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Whitham, G. B. 1965 J. Fluid Mech. 22, 273.
Whitham, G. B. 1967 J. Fluid Mech. 27, 399.
Whitham, G. B. 1974 Linear and Non-Linear Waves. Wiley, Interscience.