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Approach to local axisymmetry in a turbulent cylinder wake

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Abstract

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re d  ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re d  ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.

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Notes

  1. This may be partly due to the normalisation by the half-width L which forces all the profiles of (U ∞ – U)/U o to equal 0.5 at y  = L.

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Acknowledgments

The first author gratefully acknowledges the support of Nature Science Foundation of China through the Grant #10772006. The second author is grateful for the support of the Australian Research Council. Both authors would like to thank the referees who provided insightful comments and criticisms to an earlier version of this paper.

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Authors and Affiliations

  1. State Key Laboratory For Turbulence and Complex Systems, College of Engineering, Peking University, 100871, Beijing, China

    J. Mi

  2. Department of Energy and Resources Engineering, College of Engineering, Peking University, 100871, Beijing, China

    J. Mi

  3. Discipline of Mechanical Engineering, University of Newcastle, Newcastle, NSW, 2308, Australia

    R. A. Antonia

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  1. J. Mi
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  2. R. A. Antonia
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Correspondence to J. Mi.

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Mi, J., Antonia, R.A. Approach to local axisymmetry in a turbulent cylinder wake. Exp Fluids 48, 933–947 (2010). https://doi.org/10.1007/s00348-009-0779-2

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  • DOI: https://doi.org/10.1007/s00348-009-0779-2

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