Skip to main content
SpringerLink
Log in

Measuring intense rotation and dissipation in turbulent flows

  • Letter
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

Turbulent flows are highly intermittent—for example, they exhibit intense bursts of vorticity and strain. Kolmogorov theory1,2 describes such behaviour in the form of energy cascades from large to small spatial and temporal scales, where energy is dissipated as heat. But the causes of high intermittency in turbulence, which show non-gaussian statistics3,4,5, are not well understood. Such intermittency can be important, for example, for enhancing the mixing of chemicals6,7, by producing sharp drops in local pressure that can induce cavitation (damaging mechanical components and biological organisms)8, and by causing intense vortices in atmospheric flows. Here we present observations of the three components of velocity and all nine velocity gradients within a small volume, which allow us to determine simultaneously the dissipation (a measure of strain) and enstrophy (a measure of rotational energy) of a turbulent flow. Combining the statistics of all measurements and the evolution of individual bursts, we find that a typical sequence for intense events begins with rapid strain growth, followed by rising vorticity and a final sudden decline in stretching. We suggest two mechanisms which can produce these characteristics, depending whether they are due to the advection of coherent structures through our observed volume or caused locally.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1: Time traces of the dissipation ɛ and enstrophy Ω.
Figure 2: Distributions of the dissipation and enstrophy.
Figure 3: A scatter plot of dissipation versus enstrophy.
Figure 4: Conditional averages of the growth rate of dissipation ɛ˙.

Similar content being viewed by others

References

  1. Kolmogorov, A. N. The local structure of turbulence in the incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301–305 (1941); reprinted in Proc. R. Soc. Lond. A 434, 9–13 (1991)

    ADS  MathSciNet  Google Scholar 

  2. Kolmogorov, A. N. Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 31, 538–540 (1941); reprinted in Proc. R. Soc. Lond. A 141, 15–17 (1991)

    MATH  Google Scholar 

  3. Sreenivasan, K. R. Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid. Mech. 23, 539–600 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  4. Meneveau, C. & Sreenivasan, K. R. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1424–1427 (1987)

    Article  ADS  CAS  Google Scholar 

  5. Frisch, U. Turbulence: The Legacy of A.N. Kolmogorov 120–194 (Cambridge Univ. Press, Cambridge, 1995)

    Google Scholar 

  6. Gollub, J. P., Clarke, J., Gharib, M., Lane, B. & Mesquita, O. N. Fluctuations and transport in a stirred fluid with a mean gradient. Phys. Rev. Lett. 67, 3507–3510 (1991)

    Article  ADS  CAS  Google Scholar 

  7. Chaté, H., Villermaux, E. & Chormaz, J.-M. (eds) Mixing: Chaos and Turbulence (Kluwer Academic/Plenum, New York, 1999)

  8. Kunns, K. T. & Papoutsakis, E. T. Damage mechanisms of suspended animal cells in agitated bioreactors with and without bubble entrainment. Biotech. Bioeng. 36, 476–483 (1990)

    Article  Google Scholar 

  9. Vukoslavcevic, P., Wallace, J. M. & Balint, J.-L. The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurement by hot-wire anemometry. J. Fluid Mech. 228, 25–51 (1991)

    ADS  Google Scholar 

  10. Tao, B., Katz, J. & Meneveau, C. Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry. Phys. Fluids 12, 941–944 (2000)

    Article  ADS  CAS  Google Scholar 

  11. Tao, B., Katz, J. & Meneveau, C. Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetery measurements. J. Fluid Mech. 457, 35–78 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  12. La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019 (2001)

    Article  ADS  CAS  Google Scholar 

  13. Mordant, N., Metz, P., Michel, O. & Pinton, J.-F. Measurement of lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87, 214501 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Keane, R. D. & Adrian, R. J. Theory of cross-correlation analysis of PIV images. Appl. Sci. Res. 49, 191–215 (1992)

    Article  Google Scholar 

  15. Chen, S., Sreenivasan, K. R. & Nelkin, M. Inertial range scalings of dissipation and enstrophy in isotropic turbulence. Phys. Rev. Lett. 79, 1253–1256 (1997)

    Article  ADS  CAS  Google Scholar 

  16. Kida, S. & Ohkitani, K. Spatiotemporal intermittency and instability of a forced turbulence. Phys. Fluids A 4, 1018–1027 (1992)

    Article  ADS  CAS  Google Scholar 

  17. Majda, A. J. & Bertozzi, A. L. Vorticity and Incompressible Flow 6–13 (Cambridge Univ. Press, Cambridge, 2002)

    MATH  Google Scholar 

  18. Kostelich, E. J. Bootstrap estimates of chaotic dynamics. Phys. Rev. E 64, 016213 (2001)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the support of the National Science Foundation and the Research Corporation. R.M. and R.R. gratefully acknowledge support from the Office of Naval Research (Physics Division). We thank D. Levermore, J. Rodgers, D. DeShazer, K. R. Sreenivasan, E. Ott, T. Antonsen and J. Fineberg for advice.

Author information

Authors and Affiliations

  1. Department of Physics, IPST and IREAP, University of Maryland, College Park, Maryland, 20742-4111, USA

    Benjamin W. Zeff, Daniel D. Lanterman, Ryan McAllister, Rajarshi Roy & Daniel P. Lathrop

  2. Department of Mathematics, Arizona State University, Tempe, Arizona, 85287-1804, USA

    Eric J. Kostelich

Authors
  1. Benjamin W. Zeff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel D. Lanterman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ryan McAllister
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rajarshi Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eric J. Kostelich
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Daniel P. Lathrop
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel P. Lathrop.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeff, B., Lanterman, D., McAllister, R. et al. Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146–149 (2003). https://doi.org/10.1038/nature01334

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature01334

  • Springer Nature Limited

This article is cited by

Search

Navigation