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Article Dans Une Revue Journal of Fluid Mechanics Année : 2000

Non-local two-dimensional turbulence and Batchelor's regime for passive scalars

S. Nazarenko
  • Fonction : Auteur

Résumé

We study small-scale two-dimensional non-local turbulence, where interaction of small scales with large vortices dominates in the small-scale dynamics, by using a semi-classical approach developed in Dyachenko, Nazarenko & Zakharov (1992), Nazarenko, Zabusky & Scheidegger (1995), Dubrulle & Nazarenko (1997) and Nazarenko, Kevlahan & Dubrulle (1999). Also, we consider a closely related problem of passive scalars in Batchelor's regime, when the Schmidt number is much greater than unity. 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[minus sign]1 for turbulent energy and k1 for passive scalars. For passive scalars, the k1-spectrum was first found by Kraichnan (1974) in the special case of advection [delta]-correlated in time, and until now it was believed to correspond to an absolute thermodynamic equilibrium and not a cascade. We also obtain, both analytically and numerically, power-law spectra of decaying two-dimensional turbulence, k[minus sign]2, and passive scalar, k0.

Dates et versions

hal-00141690 , version 1 (13-04-2007)

Identifiants

Citer

S. Nazarenko, Jean-Philippe Laval. Non-local two-dimensional turbulence and Batchelor's regime for passive scalars. Journal of Fluid Mechanics, 2000, 408, pp.301-321. ⟨10.1017/S0022112099007922⟩. ⟨hal-00141690⟩

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