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Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

Published online by Cambridge University Press:  14 January 2011

ANDREAS VALLGREN
ANDREAS VALLGREN*
Affiliation:
Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: vallgren@mech.kth.se
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Abstract

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 463 - 473
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Boffetta, G. 2007 Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence. J. Fluid Mech. 589, 253.CrossRefGoogle Scholar
Borue, V. 1994 Inverse energy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 72, 1475.CrossRefGoogle ScholarPubMed
Bos, W. J. T. & Bertoglio, J.-P. 2009 Large-scale bottleneck effects in two-dimensional turbulence. J. Turbul. 10, 1.CrossRefGoogle Scholar
Bruneau, C. H. & Kellay, H. 2005 Experiments and direct numerical simulations of two-dimensional turbulence. Phys. Rev. E 71, 046305-1.CrossRefGoogle ScholarPubMed
Danilov, S. & Gurarie, D. 2001 a Forced two-dimensional turbulence in spectral and physical space. Phys. Rev. E 63, 061208.CrossRefGoogle ScholarPubMed
Danilov, S. & Gurarie, D. 2001 b Nonuniversal features of forced two-dimensional turbulence in the energy range. Phys. Rev. E 63, 020203-1.CrossRefGoogle ScholarPubMed
Elhmaidi, D., von Hardenberg, J. & Provenzale, A. 2005 Large scale dissipation and filament instability in two-dimensional turbulence. Phys. Rev. Lett. 95, 014503-1.CrossRefGoogle ScholarPubMed
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417.CrossRefGoogle Scholar
Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671.CrossRefGoogle Scholar
Maltrud, M. E. & Vallis, G. K. 1991 Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech. 228, 321.Google Scholar
Maltrud, M. E. & Vallis, G. K. 1993 Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence. Phys. Fluids A 5, 1760.CrossRefGoogle Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21.CrossRefGoogle Scholar
Nam, K., Ott, E., Antonsen, T. M. & Guzdar, P. N. 2000 Lagrangian chaos and the effect of drag on the enstrophy cascade in two-dimensional turbulence. Phys. Rev. Lett. 84, 5134.CrossRefGoogle ScholarPubMed
Paret, J. & Tabeling, P. 1998 Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Phys. Fluids 10, 3126.CrossRefGoogle Scholar
Scott, R. K. 2007 Nonrobustness of the two-dimensional turbulent inverse cascade. Phys. Rev. E 75, 046301.CrossRefGoogle ScholarPubMed
Smith, L. M. & Yakhot, V. 1994 Finite-size effects in forced two-dimensional turbulence. J. Fluid Mech. 274, 115.CrossRefGoogle Scholar
Sukoriansky, S., Galperin, B. & Chekhlov, A. 1999 Large scale drag representation in simulations of two-dimensional turbulence. Phys. Fluids 11, 3043.CrossRefGoogle Scholar
Tran, C. V. & Bowman, J. C. 2004 Robustness of the inverse energy cascade in two-dimensional turbulence. Phys. Rev. E 69, 036303.CrossRefGoogle ScholarPubMed
Verma, M. K., Ayyer, A., Debliquy, O., Kumar, S. & Chandra, A. V. 2005 Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence. Pramana 65, 297.CrossRefGoogle Scholar