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

Published online by Cambridge University Press:  28 September 2006

T. J. BRIDGES  and
N. M. DONALDSON
T. J. BRIDGES
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
N. M. DONALDSON
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 565 , 25 October 2006 , pp. 419 - 439
Copyright
© 2006 Cambridge University Press

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