Non-local two-dimensional turbulence and Batchelor's regime for passive scalars
UNSPECIFIED (2000) Non-local two-dimensional turbulence and Batchelor's regime for passive scalars. JOURNAL OF FLUID MECHANICS, 408 . pp. 301-321. ISSN 0022-1120Full text not available from this repository.
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(-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 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(-2), and passive scalar, k(0).
|Item Type:||Journal Article|
|Subjects:||T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
|Journal or Publication Title:||JOURNAL OF FLUID MECHANICS|
|Publisher:||CAMBRIDGE UNIV PRESS|
|Date:||10 April 2000|
|Number of Pages:||21|
|Page Range:||pp. 301-321|
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