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Universality of rare fluctuations in turbulence and critical phenomena

Author

Listed:
  • S. T. Bramwell

    (University College London)

  • P. C. W. Holdsworth

    (Laboratoire de Physique, Ecole Normale Suprieure)

  • J.-F. Pinton

    (Laboratoire de Physique, Ecole Normale Suprieure)

Abstract

A statistical treatment of three-dimensional turbulent flow continues to pose a challenge to theorists1,2. One suggestion invokes an analogy with equilibrium phase transitions3. Here we approach this idea experimentally, presenting evidence of a strong analogy between the statistical behaviour of a confined turbulent flow andthat of a model of the critical behaviour of a ferromagnet. Both systems experience large fluctuations limited only by the system size. We find that the power consumption measured in turbulent-flow experiments and the magnetization at the critical point of the ferromagnet have probability distributions of the same functional form, irrespective of Reynolds number on the one hand and system size on the other. The distributions both have non-gaussian tails that characterize the large-amplitude fluctuations. In this region, the scaled distributions for the two systems collapse onto a single universal curve over at least four orders of magnitude. This suggests a basic similarity in the finite-size corrections to the fluctuation statistics in the limit of infinite system size (for the magnetic system) or infinite Reynolds number (for turbulent flow).

Suggested Citation

  • S. T. Bramwell & P. C. W. Holdsworth & J.-F. Pinton, 1998. "Universality of rare fluctuations in turbulence and critical phenomena," Nature, Nature, vol. 396(6711), pages 552-554, December.
    • Handle: RePEc:nat:nature:v:396:y:1998:i:6711:d:10.1038_25083
    DOI: 10.1038/25083
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    Cited by:

    1. Reynolds, A.M., 2012. "Gusts within plant canopies are extreme value processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5059-5063.
    2. Loukidis, Andronikos & Perez-Oregon, Jennifer & Pasiou, Ermioni D. & Sarlis, Nicholas V. & Triantis, Dimos, 2021. "Similarity of fluctuations in critical systems: Acoustic emissions observed before fracture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    3. Khandakar Niaz Morshed & David Bark Jr. & Marcio Forleo & Lakshmi Prasad Dasi, 2014. "Theory to Predict Shear Stress on Cells in Turbulent Blood Flow," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-17, August.

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