Skip to main content

Small Scale Vortices in Turbulent Flows

  • Conference paper
New Approaches and Concepts in Turbulence

Part of the book series: Monte Verità ((MV))

Abstract

The evidence on small compact vortex structures in turbulent flows is summarised for various experimental and numerical flow fields. It is consistent with a model of strained almost two dimensional vortices with radii of the order of the Kolmogorov scale, and circulation Reynolds numbers of a few hundred. The known alignment properties of the strain tensor are also consistent with the kinematics of this model. A possible scenario for the generation of these structures within the “turbulent cascade is offered. The compact vortices are postulated to be essentially passive from the point of view of energy transfer, connected to the coherent structures observed in two dimensional turbulence

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ashurst, W.T., Kerstein, A.R., Kerr, R.M. & Gibson, C.H. (1987a) Alignment of vorticity and scalar gradient with strain in simulated Navier Stokes turbulence. Phys. Fluids. 30, 3243–3253.

    Google Scholar 

  • Babiano, A., Basdevant, C., Legras, B. & Sadourny, R. (1987) Vorticity and passive scalar dynamics in two dimensional turbulence. J. Fluid Mech. 183, 379–397.

    Article  Google Scholar 

  • Batchelor, G.K. (1967) An introduction to fluid mechanics, Cambridge Univ. Press, pp. 271–273.

    Google Scholar 

  • Batchelor, G.K. (1969) Computation of the energy spectrum in two dimensional turbulence. Phys. Fluids Suppl. II, 12, 233-239.

    MATH  Google Scholar 

  • Batchelor, G.K. & Townsend, A.A. (1949) The nature of turbulent motion at large wave numbers. Proc. Roy. Soc. London. A 199, 238–255.

    Article  MATH  Google Scholar 

  • Benzi, R., Paladin, G., Patarnello, S., Santangelo, P. & Vulpiani, A. (1986) Intermittency and coherent structures in two dimensional turbulence. J. Phys. A: Math. Gen. 19, 3771–3784.

    Article  MATH  Google Scholar 

  • Benzi, R., Patarnello, S. & Santangelo, P. (1987) On the statistical properties of two dimensional decaying turbulence. Europhys. Lett. 3, 811–818.

    Article  Google Scholar 

  • Betchov, R. (1956) An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497–504.

    Article  MATH  MathSciNet  Google Scholar 

  • Brachet, M.E., Meneguzzi, M., Politano, H. & Sulem, P.L. (1988) The dynamics of freely decaying two dimensional turbulence. J. Fluid Mech. 194, 333–349.

    Article  Google Scholar 

  • Callen, H.B. (1985) Thermodynamics and an introduction to thermostatics, 2nd. Ed., Wiley, pp. 203–210.

    Google Scholar 

  • Carnevale, G.F., McWilliams, J.C., Pomeau, Y., Weiss, J.B. & Young, W.R. (1991) Evolution of vortex statistics in two dimensional turbulence. Phys. Rev. Lett. 66, 2735–2737.

    Article  Google Scholar 

  • Dracos, T., Kholmyansky, M., Kit, E. & Tsinober, A. (1989) Some experimental results on velocity-velocity gradients measurements in turbulent grid flows. Proc. IUTAM Symp. Topological Fluid Mech., Cambridge, August 13–18, 1989 (H.K. Moffat and A. Tsinober, eds.), Cambridge U. Press, pp. 564–584.

    Google Scholar 

  • Douady, S., Couder, Y. & Brachet, M.E. (1991) Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.

    Article  Google Scholar 

  • Fornberg, B. (1977) A numerical study of 2D turbulence. J. Comp. Phys. 25, 1–31.

    Article  MATH  Google Scholar 

  • Hosokawa, I. & Yamamoto, K. (1990) Intermittency of dissipation in directly simulated fully developed turbulence. J. Phys. Soc. Japan. 59, 401–404.

    Article  Google Scholar 

  • Jiménez, J. (1991) Kinematic alignment effects in turbulent flows, in press Phys. Fluids A.

    Google Scholar 

  • Jiménez, J. & Moin, P. (1991) The minimal flow unit in near wall turbulence, J. Fluid Mech. 225, 213–240.

    Article  MATH  Google Scholar 

  • Kerr, R.M. (1985) Higher order derivative correlation and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.

    Article  MATH  Google Scholar 

  • Kim, J., Moin, P. & Moser, R. (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.

    Article  MATH  Google Scholar 

  • Kuo, A.Y. & Corrsin, S. (1972) Experiments on the geometry of the fine structure regions in fully turbulent fluid. J. Fluid Mech. 56, 447–479.

    Article  Google Scholar 

  • Lesieur, M. (1990) Turbulence in fluids, (2nd ed.), Kluwer, pp. 226–283.

    Google Scholar 

  • Lundgren, T.S. (1982) Strained spiral vortex model for turbulent fine structure. Phys. Fluids. 25, 2193–2203.

    Article  MATH  Google Scholar 

  • McWilliams, J.C. (1984) The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.

    Article  MATH  Google Scholar 

  • Miller, J. (1990) Statistical mechanics of Euler equation in two dimensions. Phys. Rev. Lett. 65, 2137–2140.

    Article  MATH  MathSciNet  Google Scholar 

  • Moser, R.D. & Rogers, M.M. (1991) Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids. A 3, 1128–1134.

    Article  Google Scholar 

  • Onsager, L. (1949) Statistical hydrodynamics. Nuovo Cimento Suppl. 6, 279–286.

    Article  MathSciNet  Google Scholar 

  • Robert, R. & Sommeria, J. (1991) Statistical equilibrium states for two dimensional flows. J. Fluid Mech. 229, 291–310.

    Article  MATH  MathSciNet  Google Scholar 

  • Robinson, S.K. (1989) A review of vortex structures and associated coherent motions in turbulent boundary layers. 2nd IUTAM Symp. Structure of Turbulence and Drag Reduction, Zurich, July 25–28, 1989 (A. Gyr, ed.), pp. 22–50.

    Google Scholar 

  • Rogers, M.M. & Moin, P. (1987) The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.

    Article  Google Scholar 

  • Ruetsch, G.R. & Maxey, M.R. (1991) Small scales features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids. A 3, 1587–1597.

    Article  Google Scholar 

  • Santangelo, P., Benzi, R. & Legras, B. (1989) The generation of vortices in high resolution, two dimensional decaying turbulence and the influence of initial conditions on the breaking of self similarity. Phys. Fluids. A 1, 1027–1034.

    Article  Google Scholar 

  • Schwarz, K.W. (1990) Evidence for organised small scale structure in fully developed turbulence. Phys. Rev. Lett. 64, 415–418.

    Article  Google Scholar 

  • She, Z.-S., Jackson, E. & Orszag, S.A. (1990) Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.

    Article  Google Scholar 

  • Siggia, E.D. (1981) Numerical study of small scale intermittency in three dimensional turbulence. J. Fluid Mech. 107, 375–406.

    Article  MATH  Google Scholar 

  • Van Atta, C.W. & Antonia, R.A. (1980) Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives, Phys. Fluids. 23, 252–257.

    Article  Google Scholar 

  • Vieillefosse, P. (1982) Local interaction between vorticity and shear in a perfect incompressible fluid. J. de Physique 43, 837–842

    Article  MathSciNet  Google Scholar 

  • Vincent, A. & Meneguzzi, M. (1991) The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–25.

    Article  MATH  Google Scholar 

  • Wei, T. & Willmarth, W.W. (1989) Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Basel AG

About this paper

Cite this paper

Jiménez, J. (1993). Small Scale Vortices in Turbulent Flows. In: Dracos, T., Tsinober, A. (eds) New Approaches and Concepts in Turbulence. Monte Verità. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8585-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8585-0_7

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9691-7

  • Online ISBN: 978-3-0348-8585-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics