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The interaction of skewed vortex pairs: a model for blow-up of the Navier–Stokes equations

Published online by Cambridge University Press:  25 April 2000

H. K. MOFFATT
H. K. MOFFATT
Affiliation:
Isaac Newton Institute for Mathematical Sciences, University of Cambridge, 20 Clarkson Road, Cambridge CB3 0EH, UK
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Abstract

The interaction of two propagating vortex pairs is considered, each pair being initially aligned along the positive principal axis of strain associated with the other. As a preliminary, the action of accelerating strain on a Burgers vortex is considered and the conditions for a finite-time singularity (or ‘blow-up’) are determined. The asymptotic high Reynolds number behaviour of such a vortex under non-axisymmetric strain, and the corresponding behaviour of a vortex pair, are described. This leads naturally to consideration of the interaction of the two vortex pairs, and identifies a mechanism by which blow-up may occur through self-similar evolution in an interaction zone where scale decreases in proportion to (t* − t)1/2, where t* is the singularity time. The relevance of Leray scaling in this interaction zone is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 409 , 25 April 2000 , pp. 51 - 68
Copyright
© 2000 Cambridge University Press

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