Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-11T05:56:07.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence

Published online by Cambridge University Press:  08 October 2007

G. BOFFETTA
G. BOFFETTA*
Affiliation:
Dipartimento di Fisica Generale and INFN, Università degli Studi di Torino, Via Pietro Giuria 1, 10125, Torino, Italy and CNR-ISAC, Sezione di Torino, Corso Fiume 4, 10133 Torino, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

High-resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy–enstrophy double cascade is investigated and its statistics found to be compatible with the classical Kraichnan theory in the limit of extended inertial ranges. The analysis of the joint distribution of energy and enstrophy fluxes in physical space reveals a small value of cross-correlation. This result supports many experimental and numerical studies where only one cascade is generated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 589 , 25 October 2007 , pp. 253 - 260
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bernard, D., Boffetta, G., Celani, A. & Falkovich, G. 2006 Conformal invariance in two-dimensional turbulence. Nature Phys. 2, 124.CrossRefGoogle Scholar
Boffetta, G., Celani, A., Musacchio, S. & Vergassola, M. 2002 Intermittency in two-dimensional ekman-navier-stokes turbulence. Phys. Rev. E 66, 026304.Google ScholarPubMed
Boffetta, G., Celani, A. & Vergassola, M. 2000 Inverse energy cascade in two-dimensional turbulence: Deviations from gaussian behavior. Phys. Rev. E 61, R29.Google ScholarPubMed
Borue, V. 1993 Spectral exponents of enstrophy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 71, 3967.CrossRefGoogle ScholarPubMed
Borue, V. 1994 Inverse energy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 72, 1475.CrossRefGoogle ScholarPubMed
Bruneau, C. H. & Kellay, H. 2005 Experiments and direct numerical simulations of two-dimensional turbulence. Phys. Rev. E 71, 046305.Google ScholarPubMed
Chen, S., Ecke, R. E., Eyink, G. L., Rivera, M., Wan, M. & Xiao, Z. 2006 Physical mechanism of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 96, 084502.CrossRefGoogle ScholarPubMed
Chen, S., Ecke, R. E., Eyink, G. L., Wang, X. & Xiao, Z. 2003 Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett. 91, 214501.CrossRefGoogle ScholarPubMed
Frisch, U. & Sulem, P. L. 1984 Numerical simulation of the inverse cascade in two-dimensional turbulence. Phys. Fluids 27, 1921.CrossRefGoogle Scholar
Gotoh, T. 1998 Energy spectrum in the inertial and dissipation ranges of two-dimensional steady turbulence. Phys. Rev. E 57, 2984.Google Scholar
Kellay, H., Wu, X. L. & Goldburg, W. I. 1995 Experiments with turbulent soap films. Phys. Rev. Lett. 74, 3975.CrossRefGoogle ScholarPubMed
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417.CrossRefGoogle Scholar
Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525.CrossRefGoogle Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Legras, B., Santangelo, P. & Benzi, R. 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 37.CrossRefGoogle Scholar
Lindborg, E. & Alvelius, K. 2000 The kinetic energy spectrum of the two-dimensional enstrophy turbulence cascade. Phys. Fluids 12, 945.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. 1997 Experimental observation of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 79, 4162.CrossRefGoogle Scholar
Pasquero, C. & Falkovich, G. 2002 Stationary spectrum of vorticity cascade in two-dimensional turbulence. Phys. Rev. E 65, 056305.Google ScholarPubMed
Rutgers, M. A. 1998 Forced 2d turbulence: Experimental evidence of simultaneous inverse energy and forward enstrophy cascades. Phys. Rev. Lett. 81, 2244.CrossRefGoogle Scholar
Siggia, E. & Aref, H. 1981 Point-vortex simulation of the inverse energy cascade in two-dimensional turbulence. Phys. Fluids 24, 171.CrossRefGoogle Scholar
Smith, L. & Yakhot, V. 1993 Bose condensation and small-scale structure generation in a random force driven 2d turbulence. Phys. Rev. Lett. 71, 352.CrossRefGoogle Scholar
Tabeling, P. 2002 Two-dimensional turbulence: a physicist approach. Phys. Rep. 362, 1.CrossRefGoogle Scholar