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Phys. Rev. Lett. 96, 084502 (2006) [4 pages]

Physical Mechanism of the Two-Dimensional Inverse Energy Cascade

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Shiyi Chen1,2,3,5, Robert E. Ecke3,4, Gregory L. Eyink1,2,3, Michael Rivera4, Minping Wan1, and Zuoli Xiao1
1Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA
2Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA
3Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
4Materials Science & Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
5College of Engineering, 60 Yan-Nan Yuan, Peking University, P.O. Box 100871, Beijing, China

Received 6 October 2005; published 28 February 2006

We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan’s prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from turbulent stress proportional to small-scale strain rotated by 45°. This “skew-Newtonian” stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.96.084502
DOI:
10.1103/PhysRevLett.96.084502
PACS:
47.27.Ak, 47.27.Gs, 47.27.Jv, 92.60.hk
 
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