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Vorticity and passive-scalar dynamics in two-dimensional turbulence

Published online by Cambridge University Press:  21 April 2006

Armando Babiano ,
Claude Basdevant ,
Bernard Legras  and
Robert Sadourny
Armando Babiano
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, Ecole Normale Supérieure, 75231 Paris Cedex 05, France
Claude Basdevant
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, Ecole Normale Supérieure, 75231 Paris Cedex 05, France
Bernard Legras
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, Ecole Normale Supérieure, 75231 Paris Cedex 05, France
Robert Sadourny
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, Ecole Normale Supérieure, 75231 Paris Cedex 05, France
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Abstract

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 379 - 397
Copyright
© 1987 Cambridge University Press

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