Does a particle swept by a turbulent liquid diffuse?

Moshe Schwartz*, Gad Frenkel, Sam F. Edwards

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)229-233
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 15 Mar 2014


  • Passive scalar
  • Super diffusion
  • Turbulence


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