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A model for rapid stochastic distortions of small-scale turbulence

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Dubrulle, B., Laval, J.-P., Nazarenko, Sergey and Zaboronski, Oleg V.. (2004) A model for rapid stochastic distortions of small-scale turbulence. Journal of Fluid Mechanics, Vol.520 . pp. 1-21. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112004001417

Abstract

We present a model describing the evolution of the small-scale 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 small-scale two-dimensional 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):

Navier-Stokes equations, Turbulence, Fluid mechanics, Fluid dynamics, Stochastic differential equations

Journal or Publication Title:

Journal of Fluid Mechanics

Publisher:

Cambridge University Press

ISSN:

0022-1120

Official Date:

29 November 2004

Dates:

Date	Event
29 November 2004	Published

Volume:

Vol.520

Page Range:

pp. 1-21

Identification Number:

10.1017/S0022112004001417

Status:

Peer Reviewed

Access rights to Published version:

Open Access

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