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Finite lifetime of turbulence in shear flows

Nature volume 443, pages 59–62 (2006)Cite this article

Abstract

Generally, the motion of fluids is smooth and laminar at low speeds but becomes highly disordered and turbulent as the velocity increases. The transition from laminar to turbulent flow can involve a sequence of instabilities in which the system realizes progressively more complicated states1, or it can occur suddenly2,3. Once the transition has taken place, it is generally assumed that, under steady conditions, the turbulent state will persist indefinitely. The flow of a fluid down a straight pipe provides a ubiquitous example of a shear flow undergoing a sudden transition from laminar to turbulent motion4,5,6. Extensive calculations7,8 and experimental studies9 have shown that, at relatively low flow rates, turbulence in pipes is transient, and is characterized by an exponential distribution of lifetimes. They8,9 also suggest that for Reynolds numbers exceeding a critical value the lifetime diverges (that is, becomes infinitely large), marking a change from transient to persistent turbulence. Here we present experimental data and numerical calculations covering more than two decades of lifetimes, showing that the lifetime does not in fact diverge but rather increases exponentially with the Reynolds number. This implies that turbulence in pipes is only a transient event (contrary to the commonly accepted view), and that the turbulent and laminar states remain dynamically connected, suggesting avenues for turbulence control10.

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Figure 1: Sketch of the experimental apparatus.
Figure 2: Lifetime distributions.
Figure 3: Variation of characteristic times with Reynolds number.

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Acknowledgements

This work was funded through a RCUK fellowship (B.H.), the Foundation of Fundamental Research on Matter (J.W.) and Deutsche Forschungsgemeinschaft (T.M.S. and B.E.). B.H. and J.W. thank R. Delfos for discussions and W. Tax and P. Tipler for technical assistance. We thank the Dorset Tube Company for supplying the precision pipe.

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Authors and Affiliations

  1. School of Physics and Astronomy, The University of Manchester, M13 9PL, Manchester, UK

    Björn Hof

  2. Laboratory for Aero & Hydrodynamics, Delft University of Technology, 2628 CA, Delft, The Netherlands

    Björn Hof & Jerry Westerweel

  3. Hydrodynamics, Delft University of Technology, 2628 CA

    Björn Hof & Jerry Westerweel

  4. Fachbereich Physik, Philipps-Universität Marburg, 35032, Marburg, Germany

    Tobias M. Schneider & Bruno Eckhardt

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  1. Björn Hof
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  2. Jerry Westerweel
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  3. Tobias M. Schneider
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  4. Bruno Eckhardt
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Correspondence to Björn Hof.

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Supplementary information

Supplementary Data

DIn this supplement we provide further information on various aspects of the experiment, of the numerical simulations and an account of the re-analysis of the data for plane Couette flow that could not be included in the main text. Also included are supplementary figures 1–4. (PDF 221 kb)

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Hof, B., Westerweel, J., Schneider, T. et al. Finite lifetime of turbulence in shear flows. Nature 443, 59–62 (2006). https://doi.org/10.1038/nature05089

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