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A model for rapid stochastic distortions of smallscale turbulence
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Dubrulle, B., Laval, J.P., Nazarenko, Sergey and Zaboronski, Oleg V.. (2004) A model for rapid stochastic distortions of smallscale turbulence. Journal of Fluid Mechanics, Vol.520 . pp. 121. ISSN 00221120

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Official URL: http://dx.doi.org/10.1017/S0022112004001417
Abstract
We present a model describing the evolution of the smallscale Navier–Stokes turbulence due to its stochastic distortion by much larger turbulent scales. This study is motivated by numerical findings (Laval et al. Phys. Fluids vol. 13, 2001, p. 1995) that such interactions of separated scales play an important role in turbulence intermittency. We introduce a description of turbulence in terms of the moments of $k$space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko et al. Phys. Rev. E vol. 68, 2003, 0266311). Working with the $k$space moments allows us to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the smallscale twodimensional turbulence shows that the Fourier moments take their Gaussian values in the energy cascade range whereas the enstrophy cascade is intermittent. In three dimensions, we show that the statistics of turbulence wavepackets deviates from Gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$space centred at its origin and having one large, one neutral and one small axis with the velocity field pointing parallel to the smallest axis.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  NavierStokes equations, Turbulence, Fluid mechanics, Fluid dynamics, Stochastic differential equations 
Journal or Publication Title:  Journal of Fluid Mechanics 
Publisher:  Cambridge University Press 
ISSN:  00221120 
Official Date:  29 November 2004 
Volume:  Vol.520 
Page Range:  pp. 121 
Identification Number:  10.1017/S0022112004001417 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Balkovsky, E. & Fouxon, A. 1999 Universal longtime properties of lagrangian statistics in the 
URI:  http://wrap.warwick.ac.uk/id/eprint/758 
Data sourced from Thomson Reuters' Web of Knowledge
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