Journal of Fluid Mechanics


Acceleration statistics of heavy particles in turbulence

a1 CNRS Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
a2 Department of Physics and INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
a3 Department of Physics and INFN, University of Torino, Via Pietro Giuria 1, 10125, Torino, Italy
a4 CNRS, INLN, 1361 Route des Lucioles, F-06560 Valbonne, France
a5 SMC-INFM c/o Department of Physics, University of Rome “La Sapienza”, Piazz.le A. Moro, 2, I-00185 Roma, Italy, and CNR-ISC via dei Taurini 19, I-00185 Roma, Italy
a6 CNR-ISAC, Sezione di Lecce, Str. Prov. Lecce-Monteroni km 1,200, I-73100 Lecce, Italy
a7 Department of Physics, University of Rome “La Sapienza”, Piazz.le A. Moro, 2, I-00185 Roma, Italy
a8 CNR-IAC, Viale del Policlinico 137, I-00161 Roma, Italy and INFN, Sezione di Ferrara, via G. Saragat 1, I-44100, Ferrara, Italy

Article author query
bec j   [Google Scholar] 
biferale l   [Google Scholar] 
boffetta g   [Google Scholar] 
celani a   [Google Scholar] 
cencini m   [Google Scholar] 
lanotte a   [Google Scholar] 
musacchio s   [Google Scholar] 
toschi f   [Google Scholar] 


We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, St, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: (i) the root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value at quite small Stokes numbers; (ii) at a given St the normalized acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; (iii) the tails of the probability density function of the normalized acceleration $a/a_{\rm rms}$ decrease with St. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small St, and filtering induced by the particle response time, that takes over at larger St.

(Published Online February 27 2006)
(Received August 5 2005)
(Revised December 9 2005)