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Euler–Poincaré formulation and elliptic instability for nth-gradient fluids

Bruce R Fabijonas1 and Darryl D Holm2,3

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The energy of an nth-gradient fluid depends on its Eulerian velocity gradients of order n. A variational principle is introduced for the dynamics of nth-gradient fluids and their properties are reviewed in the context of Noether's theorem. The stability properties of Craik–Criminale solutions for first and second gradient fluids are examined.


PACS

47.50.-d Non-Newtonian fluid flows

47.10.-g General theory in fluid dynamics

MSC

76M30 Variational methods

76A05 Non-Newtonian fluids

Subjects

Fluid dynamics

Mathematical physics

Dates

Issue 30 (30 July 2004)

Received 26 February 2004, in final form 21 May 2004

Published 14 July 2004



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