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Invariants in dissipationless hydrodynamic media

Published online by Cambridge University Press:  26 April 2006

A. V. Tur  and
V. V. Yanovsky
A. V. Tur
Affiliation:
Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, 2 Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre Les Nancy, Cedex France
V. V. Yanovsky
Affiliation:
Electro-Physical Scientifique Centre, The Ukrainian Academy of Sciences, Kharkov, Ukraine 310108
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Abstract

We propose a general geometric method of derivation of invariant relations for hydrodynamic dissipationless media. New dynamic invariants are obtained. General relations between the following three types of invariants are established, valid in all models: Lagrangian invariants, frozen-in vector fields and frozen-in co-vector fields. It is shown that frozen-in integrals form a Lie algebra with respect to the commutator of the frozen fields. The relation between frozen-in integrals derived here can be considered as the Backlund transformation for hydrodynamic-type systems of equations. We derive an infinite family of integral invariants which have either dynamic or topological nature. In particular, we obtain a new type of topological invariant which arises in all hydrodynamic dissipationless models when the well-known Moffatt invariant vanishes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 67 - 106
Copyright
© 1993 Cambridge University Press

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