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Non-local 2D turbulence and Batchelor's regime for passive scalars

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2000
auteur(s) Nazarenko Sergey V.; Laval Jean-Philippe
journal (abréviation) Journal of Fluid Mechanics (J. Fluid Mech.)
volume (numéro) 408
  
pages 301 – 321
résumé A semi-classical approach has recently been developed to describe dynamics of small scales advected by a large-scale flow. Depending on the situation, the small scales may be dispersive or non-dispersive waves, 2D vorticity or 3D potential vorticity. In this paper, we consider small-scale 2D non-local turbulence, where interaction of small scales with large vortices dominates in the small-scale dynamics. Also, we consider a closely related problem of passive scalars in Batchelor's regime, when the Peclet number is much greater than the Reynolds number. In our approach, we do not perform any statistical averaging, and most of our results are valid for any form of the large-scale advection. A new invariant is found in this paper for passive scalars when their initial spectrum is isotropic. It is shown, analytically, numerically and using a dimensional argument, that there is a spectrum corresponding to an inverse cascade of the new invariant, which scales like k^(-1) for turbulent energy and k^1 for passive scalars. For passive scalars, the k^1-spectrum was first found by Kraichnan (1974) in the special case of delta-correlated in time advection, and until now it was believed to be corresponding to an absolute thermodynamical equilibrium and not a cascade.We also obtain, both analytically and numerically, power-law spectra of decaying 2D turbulence, k^(-2), and passive scalar, k^0.
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