Variational formulations for steady water waves with vorticity

For free-surface water flows with a vorticity that is monotone with depth, we show that any critical point of a functional representing the total energy of the flow adjusted with a measure of the vorticity, subject to the constraints of fixed mass and horizontal momentum, is a steady water wave.

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 548; pp. 151 - 163
Main Authors CONSTANTIN, ADRIAN, SATTINGER, DAVID, STRAUSS, WALTER
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.02.2006
Subjects
Exact sciences and technology
Fluid dynamics
Free surfaces
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Physics
Surface water
Water depth
Water flow
Water waves
Wave propagation
Variational methods
Critical points
Vorticity
Periodic oscillation
Free surface flow
Shallow water
Online AccessGet full text
ISSN0022-1120
1469-7645
DOI10.1017/S0022112005007469

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Summary:For free-surface water flows with a vorticity that is monotone with depth, we show that any critical point of a functional representing the total energy of the flow adjusted with a measure of the vorticity, subject to the constraints of fixed mass and horizontal momentum, is a steady water wave.
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ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112005007469