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Vortex dynamics in perfect fluids

Published online by Cambridge University Press:  13 March 2009

Yves Pomeau
Yves Pomeau
Affiliation:
Laboratoire de Physique Statistique, associé an CNRS, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France, and Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
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Abstract

I review the current status of a problem, relevant to both plasma physics and ordinary fluid mechanics, namely the long-time behaviour of solutions of the perfect fluid equations. In two space dimensions, thanks in particular to the work of D. Montgomery, the situation is now quite clear, since one expects the formation at long times of large vortices in a background of potential flow. In three dimensions, the situation is blurred, although its understanding is a central issue for fully developped turbulence. I present some new estimates for a possible scenario of self-similar blow up of solutions of 3D Euler. That turns out to be a rather subtle question, if one tries to stay consistent with the conservation of circulation and of energy.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 407 - 418
Copyright
Copyright © Cambridge University Press 1996

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References

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