Surface waves on steady perfect-fluid flows with vorticity

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this theory of two-dimensional steady periodic surface waves on flows under gravity, the functional dependence of vorticity on the stream function is a priori unknown. It is shown that when the vorticity distribution function is given, weak solutions arise from minimization of the total energy. The fact that vorticity is indeed a function of the stream function is then an infinite-dimensional Lagrange multiplier rule, the consequence of minimizing energy subject to the vorticity distribution function being prescribed.

To illustrate the idea with a minimum of technical difficulties, the existence of non-trivial waves with a prescribed distribution of vorticity on the surface of a fluid confined beneath an elastic sheet is proved. The theory does not distinguish between irrotational waves and waves with locally square-integrable vorticity.

Original languageEnglish
Pages (from-to)975-1007
Number of pages33
JournalCommunications on Pure and Applied Mathematics
Volume64
Issue number7
Early online date14 Mar 2011
DOIs
Publication statusPublished - Jul 2011

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Perfect Fluid
Surface Waves
Vorticity
Surface waves
Fluid Flow
Flow of fluids
Stream Function
Distribution functions
Distribution Function
Lagrange multiplier Rule
Periodic Wave
Lagrange multipliers
Energy
Weak Solution
Gravity
Gravitation
Fluid
Unknown
Fluids

Cite this

Surface waves on steady perfect-fluid flows with vorticity. / Burton, Geoffrey R; Toland, John F.

In: Communications on Pure and Applied Mathematics, Vol. 64, No. 7, 07.2011, p. 975-1007.

Research output: Contribution to journalArticle

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