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Vortical control of forced two-dimensional turbulence

Fontane, Jérôme and Dritschel, David and Scott, Richard Vortical control of forced two-dimensional turbulence. (2013) Physics of Fluids, 25 (1). ISSN 1089-7666

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Official URL: http://link.aip.org/link/doi/10.1063/1.4774336

Abstract

A new numerical technique for the simulation of forced two-dimensional turbulence (Dritschel and Fontane, 2010) is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods,making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott (2007), namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k^(−2) is obtained in place of the classical k^(−5/3) prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t^(−1) rather than Kraichnan’s prediction of t^(−3/2). The deviation from Kraichnan’s theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.

Item Type:Article
Additional Information:Thanks to American Institute of Physics. The definitive version is available at AIP website: http://pof.aip.org/resource/1/phfle6/v25/i1/p015101_s1
HAL Id:hal-00786342
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > University of St Andrews (UNITED KINGDOM)
Laboratory name:
Funders:
European Community, Marie Curie Fellowship
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Deposited By: Jérôme Fontane
Deposited On:08 Feb 2013 12:58

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