Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T09:47:57.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Coherent vortices and tracer cascades in two-dimensional turbulence

Published online by Cambridge University Press:  15 February 2007

ARMANDO BABIANO  and
ANTONELLO PROVENZALE
ARMANDO BABIANO
Affiliation:
Laboratoire de Météorologie Dynamique, Département de Géophysique de l'ENS de Paris, 24, rue Lhomond, 75005, Paris, Francebabiano@lmd.ens.fr
ANTONELLO PROVENZALE
Affiliation:
Istituto di Scienze dell'Atmosfera e del Clima, CNR, Corso Fiume 4, 10133 Torino, Italya.provenzale@isac.cnr.it
Get access Rights & Permissions [Opens in a new window]

Abstract

We study numerically the scale-to-scale transfers of enstrophy and passive-tracer variance in two-dimensional turbulence, and show that these transfers display significant differences in the inertial range of the enstrophy cascade. While passive-tracer variance always cascades towards small scales, enstrophy is characterized by the simultaneous presence of a direct cascade in hyperbolic regions and of an inverse cascade in elliptic regions. The inverse enstrophy cascade is particularly intense in clusters of small-scales elliptic patches and vorticity filaments in the turbulent background, and it is associated with gradient-decreasing processes. The inversion of the enstrophy cascade, already noticed by Ohkitani (Phys. Fluids A, vol. 3, 1991, p. 1598), appears to be the main difference between vorticity and passive-tracer dynamics in incompressible two-dimensional turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 429 - 448
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

Babiano, A., Basdevant, C., Legras, B. & Sadourny, R. 1987 Vorticity and passive scalar dynamics in two-dimensional turbulence. J. Fluid Mech. 183, 379–397.CrossRefGoogle Scholar
Babiano, A. & Dubos, T. 2005 On the contribution of coherent vortices to the two-dimensional inverse energy cascade. J. Fluid Mech. 529, 97–115.CrossRefGoogle Scholar
Basdevant, C. & Philipovitch, T. 1994 On the validity of the “Weiss criterion” in two-dimensional turbulence. Physica D 73, 17–30.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence Phys. Fluids Suppl. 12, II 233–133.CrossRefGoogle Scholar
Bracco, A., Lacasce, J., Pasquero, C. & Provenzale, A. 2000 a The velocity distribution of barotropic turbulence. Phys. Fluid. 12, 2478–2488.CrossRefGoogle Scholar
Bracco, A., McWilliams, J. C., Murante, G., Provenzale, A. & Weiss, J. B. 2000 b Revisiting freely-decaying two-dimensional turbulence at millennial resolution. Phys. Fluid. 12, 2931–2941.CrossRefGoogle Scholar
Dubos, T. & Babiano, A. 2002 Two-dimensional cascades and mixing: a physical space apprach. J. Fluid Mech. 467, 81–100.CrossRefGoogle Scholar
Dubos, T. & Babiano, A. 2003 Comparing the two-dimensional cascades of vorticity and a passive scalar. J. Fluid Mech. 492, 131–145.CrossRefGoogle Scholar
Elhmaidi, D., von Hardenberg, J. & Provenzale, A. 2005 Large-scale dissipation and filament instability in two-dimensional turbulence. Phys. Rev. Lett. 95, 014503.CrossRefGoogle ScholarPubMed
Elhmaidi, D., Provenzale, A. & Babiano, A. 1993 Elementary topology of two-dimensional turbulence from a Lagrangian viewpoint and single-particle dispersion. J. Fluid Mech. 257, 533–558.CrossRefGoogle Scholar
Holloway, G. & Krismannsson, S. S. 1984 Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech. 141, 27–50.CrossRefGoogle Scholar
Hua, B. L. & Klein, P. 1998 An exact criterion for the stirring properties of nearly two-dimensional turbulence. Physica D 113, 98–110.Google Scholar
Jullien, M.-C., Castiglione, P. & Tabeling, P. 2000 Experimental observation of Batchelor dispersion of passive tracers. Phys. Rev. Lett. 85, 3636.CrossRefGoogle ScholarPubMed
Kimura, Y. & Herring, J. R. 2001 Gradient enhancement and filament ejection for a non-uniform elliptic vortex in two-dimensional turbulence. J. Fluid Mech. 439, 43–56.CrossRefGoogle Scholar
Klein, P., Hua, B. L. & Lapeyre, G. 2000 Alignment of tracer gradient vectors in two-dimensional turbulence. Physica D 146, 246–260.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluid. 10, 1417–1423.CrossRefGoogle Scholar
Landau, L. & Lifshitz, E. 1971 Mécanique des Fluides. Édition Mir.Google Scholar
Lapeyre, G., Hua, B. L. & Klein, P. 2001 Dynamics of the orientation of gradients of passive and active scalar in two-dimensional turbulence. Phys. Fluid. 13, 251–264.CrossRefGoogle Scholar
Lapeyre, G., Klein, P. & Hua, B. L. 1999 Does the tracer gradient align with the strain eigenvectors in 2D turbulence? Phys. Fluid. 11, 3729–3737.CrossRefGoogle Scholar
Larchevque, M. 1993 Pressure field and coherent structures in two-dimensional incompressible turbulent flows. Theor. Comput. Fluid Dyn. 5, 215–222.CrossRefGoogle Scholar
Lesieur, M. & Herring, J. 1985. Diffusion of a passive scalar in two-dimensional turbulence. J. Fluid Mech. 161, 77–95.CrossRefGoogle Scholar
Lindborg, E. 1999 Can the atmospheric kinetic energy spestrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259–288.CrossRefGoogle Scholar
Lindborg, E. & Alvelius, K. 2000 The kinetic energy spectrum of the two-dimensional enstrophy turbulent cascade. Phys. Fluid. 12, 945–947.CrossRefGoogle Scholar
McWilliams, J. 1984 The emergence of isolated coherent vortices in turbulent flows. J. Fluid Mech. 146, 21–43.CrossRefGoogle Scholar
McWilliams, J. 1990 The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361–385.CrossRefGoogle Scholar
Ohkitani, K. 1991 Wave number space dynamics of enstrophy cascade in a forced 2-dimensional turbulence. Phys. Fluids A 3, 1598–1611.CrossRefGoogle Scholar
Okubo, A. 1970 Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergence. Deep-Sea Res. 17, 445–454.Google Scholar
Paret, J. & Tabeling, P. 1998 Intermittency in the two-dimensional inverse cascade of energy: Experimental observations. Phys. Fluid. 10, 3126–3136.CrossRefGoogle Scholar
Pasquero, C., Provenzale, A. & Babiano, A. 2001 Parameterization of dispersion in two-dimensional turbulence. J. Fluid Mech. 439, 279–303.CrossRefGoogle Scholar
Protas, B., Babiano, A. & Kevlahan, N. K. R. 1999 On geometrical alignment properties of two-dimensional forced turbulence. Physica D 128, 169–179.Google Scholar
Weiss, J. 1991 The dynamics of the enstrophy transfer in two-dimensional turbulence. Physica D 48, 273–294.Google Scholar
Yaglom, A. M. 1949 On the local structure of a temperature field in a turbulent flow. Dokl. Akad. Nauk. SSS. 69, 743.Google Scholar