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The dynamics of freely decaying two-dimensional turbulence

Published online by Cambridge University Press:  21 April 2006

M. E. Brachet ,
M. Meneguzzi ,
H. Politano  and
P. L. Sulem
M. E. Brachet
Affiliation:
CNRS, G.P.S., Ecole Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05, France CNRS, Observatoire de Nice, B.P. 239, 06007 Nice Cedex, France
M. Meneguzzi
Affiliation:
CNRS, Service d'Astrophysique, C.E.N.-Saclay, 91191 Saclay, France
H. Politano
Affiliation:
CNRS, Observatoire de Nice, B.P. 239, 06007 Nice Cedex, France
P. L. Sulem
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, 69978 Tel Aviv. Israel
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Abstract

Direct numerical simulations of decaying high-Reynolds-number turbulence are presented at resolutions up to 8002 for general periodic flows and 20482 for periodic flows with large-scale symmetries. For turbulence initially excited at large scales, we characterize a transition of the inertial energy-spectrum exponent from n ≈ − 4 at early times to n ≈ − 3 when the turbulence becomes more mature. In physical space, the first regime is associated with isolated vorticity-gradient sheets, as predicted by Saffman (1971). The second regime, which is essentially statistical, corresponds to an enstrophy cascade (Kraichnan 1967; Batchelor 1969) and reflects the formation of layers resulting from the packing of vorticity-gradient sheets. In addition to these small-scale structures, the simulation displays vorticity macro-eddies which will survive long after the vorticity-gradient layers have been dissipated (McWilliams 1984). We validate the linear description of two-dimensional turbulence suggested by Weiss (1981), which predicts that coherent vortices will survive in regions where vorticity dominates strain, while vorticity-gradient sheets will be formed in regions where strain dominates. We show that this analysis remains valid even after vorticity-gradient sheets have been formed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 333 - 349
Copyright
© 1988 Cambridge University Press

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