Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence

Laurent Chevillard; Charles Meneveau

doi:10.1016/j.crme.2007.03.002

Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence

Presented by: Geneviève Comte-Bellot

Laurent Chevillard ¹; Charles Meneveau ¹

¹ Department of Mechanical Engineering, the Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA

Comptes Rendus. Mécanique, Volume 335 (2007) no. 4, pp. 187-193.

Abstract
Résumé

The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation time-scale and forcing strength. Numerical tests show that the same (universal) anomalous relative scaling exponents are obtained for the three model variants. It is also found that transverse velocity gradients are more intermittent than longitudinal ones, whereas dissipation and enstrophy scale with the same exponents. The results are consistent with the universality of intermittency and relative scaling exponents, and suggest that these are dictated by the self-stretching terms that are the same in each variant of the model.

Le caractère universel du phénomène d'intermittence en turbulence est étudié à partir d'un modèle récent régissant l'évolution du tenseur des gradients de vitesse. Trois versions possibles du modèle, pour lesquelles les hypothèses retenues pour le temps de corrélation et l'amplitude du forçage sont différentes, sont analysées. Une intégration numérique des équations montre que les exposants anormaux des moments relatifs sont les mêmes pour les trois variantes du modèle. Il est de plus montré que les gradients transversaux de vitesse sont plus intermittents que les longitudinaux alors que la dissipation et l'enstrophie se comportent comme des lois de puissance de même exposant. Ces résultats sont cohérents avec l'universalité des exposants relatifs et suggèrent l'importance du terme d'auto-étirement, qui est identique dans les trois variantes du modèle.

Received: 2007-01-20
Accepted: 2007-03-13
Published online: 2007-04-01

DOI: 10.1016/j.crme.2007.03.002

Keywords: Turbulence, Intermittency, Geometry
Mot clés : Turbulence, Intermittence, Géométrie

Author's affiliations:

Laurent Chevillard ¹; Charles Meneveau ¹

¹ Department of Mechanical Engineering, the Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA

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     author = {Laurent Chevillard and Charles Meneveau},
     title = {Intermittency and universality in a {Lagrangian} model of velocity gradients in three-dimensional turbulence},
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     pages = {187--193},
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     doi = {10.1016/j.crme.2007.03.002},
     language = {en},
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Laurent Chevillard; Charles Meneveau. Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence. Comptes Rendus. Mécanique, Volume 335 (2007) no. 4, pp. 187-193. doi : 10.1016/j.crme.2007.03.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.03.002/

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