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On averaged equations for finite-amplitude water waves

Published online by Cambridge University Press:  19 April 2006

M. Stiassnie  and
D. H. Peregrine
M. Stiassnie
Affiliation:
School of Mathematics, University of Bristol Permanent address: Technion, Israel Institute of Technology, Haifa, Israel.
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol
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Abstract

The wave-action conservation equation for water waves is always derived from a Lagrangian for irrotational flow. This is quite satisfactory if the whole flow-field (i.e. waves and background current) is irrotational, but is inadequate for a background current with a large-scale (vertical) vorticity, even if the flow has negligible vorticity on the local scale of a few wavelengths. A wave-action conservation equation is derived for this case and equations governing the flow and the waves are given in a simple form closely parallel to the irrotational flow equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 3 , 16 October 1979 , pp. 401 - 407
Copyright
© 1979 Cambridge University Press

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References

Andrews, D. G. & McIntyre, M. E. 1978a An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609–646.Google Scholar
Andrews, D. G. & McIntyre, M. E. 1978b On wave-action and its relatives. J. Fluid Mech. 89, 647–664.Google Scholar
Crapper, G. D. 1979 Energy and momentum integrals for progressive capillary-gravity waves. J. Fluid Mech. 94, 13–24.Google Scholar
Cokelet, E. D. 1977 Steep gravity waves in water of arbitrary uniform depth. Phil. Trans. Roy. Soc. A 286, 183–230.Google Scholar
Jonsson, I. G. 1978 Energy flux and wave action in gravity waves propagating on a current. J. Hydraul. Res. 16, 223–234.Google Scholar
Longuet-Higgins, M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. Soc. A 342, 157–174.Google Scholar
Peregrine, D. H. 1976 Interactions of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Peregrine, D. H. & Thomas, G. P. 1979 Finite-amplitude deep-water waves on currents. Phil. Trans. Roy. Soc. A 292, 371–390.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Whitham, G. B. 1974 Linear and Non-Linear Waves. Wiley-Interscience.