TY - JOUR

T1 - Does a particle swept by a turbulent liquid diffuse?

AU - Schwartz, Moshe

AU - Frenkel, Gad

AU - Edwards, Sam F.

PY - 2014/3/15

Y1 - 2014/3/15

N2 - 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.

AB - 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.

KW - Passive scalar

KW - Super diffusion

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=84892161504&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2013.12.020

DO - 10.1016/j.physa.2013.12.020

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AN - SCOPUS:84892161504

SN - 0378-4371

VL - 398

SP - 229

EP - 233

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -