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Scalar turbulence

Nature volume 405, pages 639–646 (2000)Cite this article

Abstract

The advection of a passive substance by a turbulent flow is important in many natural and engineering settings. The concentration of such a substance can exhibit complex dynamic behaviour that shows many phenomenological parallels with the behaviour of the turbulent velocity field. Yet the statistical properties of this so-called ‘passive scalar’ turbulence are decoupled from those of the underlying velocity field. Passive scalar turbulence has recently yielded to mathematical analysis, and such progress may ultimately lead to a better understanding of the still intractable problem of fluid turbulence itself.

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Figure 1: Fluorescent dye in a turbulent jet.
Figure 2: Probability distribution functions (PDF).
Figure 3: Scalar fluctuations in time and space.
Figure 4: Anomalous scaling exponent, 2ζ2 - ζ4, versus scaling index γ (see equation (2)).
Figure 5: Contribution of fronts and configuration dependence of the three-point correlator.

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Acknowledgements

The authors have greatly benefited from interactions with colleagues, and are particularly grateful to S. Chen, K. Sreenivasan, P. Tabeling, Z. Warhaft and L. Mydlarski for contributing to the figures.

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Authors and Affiliations

  1. Bell Laboratories, Lucent Technologies , Murray Hill, 07974, New Jersey, USA

    Boris I. Shraiman

  2. Center for Physics and Biology, Rockefeller University, New York, 10021, New York, USA

    Eric D. Siggia

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  1. Boris I. Shraiman
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  2. Eric D. Siggia
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Shraiman, B., Siggia, E. Scalar turbulence. Nature 405, 639–646 (2000). https://doi.org/10.1038/35015000

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