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Does a particle swept by a turbulent liquid diffuse?

Author

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  • Schwartz, Moshe
  • Frenkel, Gad
  • Edwards, Sam F.

Abstract

We consider a particle swept by ordinary turbulent flow and find that its mean square displacement (MSD) is not linear in the traversed time, T, which would correspond to diffusion, but rather it is proportional to T raised to the power 6/5, for large times. This behavior stems from correlations of the velocity field, on length scales much larger than the largest scale corresponding to the inertial range. We derive our results using two different methods. The first employs an analytic self consistent path integral formulation for obtaining the statistics of the trajectory of a swept particle, given the correlations of the flow. The second involves a numerical solution of an integro-differential equation for the MSD. The conditions which make it possible to observe this behavior are discussed. A by-product of our considerations is the general large T behavior of the MSD for a large family of flows, which includes ordinary turbulence as a special case.

Suggested Citation

  • Schwartz, Moshe & Frenkel, Gad & Edwards, Sam F., 2014. "Does a particle swept by a turbulent liquid diffuse?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 229-233.
    • Handle: RePEc:eee:phsmap:v:398:y:2014:i:c:p:229-233
    DOI: 10.1016/j.physa.2013.12.020
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    Citations

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    Cited by:

    1. Shuyun Ren & Hau-Ling Chan & Pratibha Ram, 2017. "A Comparative Study on Fashion Demand Forecasting Models with Multiple Sources of Uncertainty," Annals of Operations Research, Springer, vol. 257(1), pages 335-355, October.
    2. Frenkel, Gad, 2015. "Droplet shape fluctuations in agitated emulsions—Beyond the dilute limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 251-261.

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