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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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