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Secondary criticality of water waves. Part 2. Unsteadiness and the Benjamin–Feir instability from the viewpoint of hydraulics

Bridges, T.J. and Donaldson, N. M. (2006) Secondary criticality of water waves. Part 2. Unsteadiness and the Benjamin–Feir instability from the viewpoint of hydraulics Journal of Fluid Mechanics, 565. pp. 419-439. ISSN 0022-1120

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Abstract

The theory for criticality presented in Part 1 is extended to the unsteady problem, and a new formulation of the Benjamin–Feir instability for Stokes waves in finite depth coupled to a mean flow, which takes the criticality matrix as an organizing centre, is presented. The generation of unsteady dark solitary waves at points of stability changes and their connection with the steady dark solitary waves of Part 1 are also discussed.

Item Type: Article
Additional Information: Published in Journal of Fluid Mechanics, 565, 419-439. © 2006 Cambridge University Press. Reprinted with permission.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 07 Nov 2013 13:37
URI: http://epubs.surrey.ac.uk/id/eprint/1553

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