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Steady three-dimensional water-wave patterns on a finite-depth fluid

Bridges, Thomas J., Dias, F. and Menasce, D. (2001) Steady three-dimensional water-wave patterns on a finite-depth fluid Journal of Fluid Mechanics.


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The formation of doubly-periodic patterns on the surface of a fluid layer with a uniform velocity field and constant depth is considered. The fluid is assumed to be inviscid and the flow irrotational. The problem of steady patterns is shown to have a novel variational formulation, which includes a new characterization of steady uniform mean flow, and steady uniform flow coupled with steady doubly periodic patterns. A central observation is that mean flow can be characterized geometrically by associating it with symmetries. The theory gives precise information about the role of the ten natural parameters in the problem which govern the wave–mean flow interaction for steady patterns in finite depth. The formulation is applied to the problem of interaction of capillary–gravity short-crested waves with oblique travelling waves, leading to several new observations for this class of waves. Moreover, by including oblique travelling waves and short-crested waves in the same analysis, new bifurcations of short-crested waves are found, which give rise to mixed waves which may have complicated spatial structure.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bridges, Thomas
Dias, F.
Menasce, D.
Date : 22 June 2001
Additional Information : Published in the Journal of Fluid Mechanics (2001), 436:145-175. Copyright © 2001 Cambridge University Press. Reprinted with permission. Click here to visit the journal site.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 16 Jan 2019 16:22

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