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Stretched vortices – the sinews of turbulence; large-Reynolds-number asymptotics

Published online by Cambridge University Press:  26 April 2006

H. K. Moffatt ,
S. Kida  and
K. Ohkitani
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
S. Kida
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan
K. Ohkitani
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan
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Abstract

A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in ε = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(ε2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in ε is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 259 , 25 January 1994 , pp. 241 - 264
Copyright
© 1994 Cambridge University Press

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