Interaction of localised packets of vorticity with turbulence

  • A. Leonard
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)


The evolution of initially weak structures of vorticity as they evolve in an incompressible turbulent flow is investigated. Such objects are candidates for important structures in the inertial range and in the dissipation range of scales. As these structures are strained by the flow, fine-scales of vorticity are produced along the direction of maximum compression with a consequent flow of energy to the high wavenumbers. It is shown that, under certain circumstances, the self-energy spectrum of such a structure may be time-averaged, producing a fractional power law. The exponent of the power law depends on the ratio of the first two Lyapunov exponents of the strain tensor.


Lyapunov Exponent Vortex Ring Vortex Tube Inertial Range Chaotic Advection 
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  1. Bayly, B. J. 2001 Asymptotic structure of fast dynamo eigenfunctions. Proceedings IUTAM ZakopaneGoogle Scholar
  2. Cambon, C. & Scott, J. F. 1999 Linear and nonlinear models of anisotropic turbulence. Ann. Rev. of Fluid Mech.31, 1–53.MathSciNetADSCrossRefGoogle Scholar
  3. Chertov, M., Falkovich, G., Kolokolov, I., & Vergassola, M. 1999 Small-scale turbulent dynamo. Phys. Rev. Lett.83, 4065–68.ADSCrossRefGoogle Scholar
  4. Galluccio, S. & Vulpiani, A. 1994 Stretching of material lines and surfaces in systems with Lagrangian chaos. Physica A212:,(1–2) 75–98.ADSCrossRefGoogle Scholar
  5. Gilbert, A. D. 1993 A cascade interpretation of Lundgren’s stretched spiral vortex model for turbulent fine structure. Phys. Fluids A5, 2831–2834.CrossRefMathSciNetzbMATHADSGoogle Scholar
  6. Girimaji, S. S. & Pope, S. B. 1990 Material-element deformation in isotropic turbulence. J. Fluid Mech.220, 427–458.ADSCrossRefGoogle Scholar
  7. Kida, S., Goto, S. & Makihara, T. 2002 Low-pressure vortex analysis in turbulence: Life, structure, and dynamical role of vortices. Proceedings IUTAM ZakopaneGoogle Scholar
  8. Leonard, A. 2000 Evolution of localized packets of vorticity and scalar in turbulence. In Turbulence Structure and Vortex Dynamics (ed. J. Hunt & J. Vassilicos), pp. 127–139. Cambridge University Press.Google Scholar
  9. Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids25, 2193–2203.CrossRefzbMATHADSGoogle Scholar
  10. Pearson, J. R. A. 1959 The effect of uniform distortion on weak homogeneous turbulence. J. Fluid Mech.5, 274–288.MathSciNetzbMATHADSCrossRefGoogle Scholar
  11. Reyl, C. & Antonsen Jr., T. M. 1998 Vorticity generation by instabilities of chaotic fluid flows. Physica D111, 202–226.CrossRefMathSciNetADSzbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • A. Leonard
    • 1
  1. 1.Graduate Aeronautical LaboratoriesCalifornia Institute of TechnologyPasadenaUSA

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