Acceleration statistics of heavy particles in turbulence

Abstract

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: ({\it i}) The root-mean-squared acceleration $a_{\mathrm{rms}}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\mathrm{rms}}/({\epsilon }^3/\nu {)}^{1/4}$ increases with $R_{\lambda }$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\mathrm{rms}}$ 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 $St$.

10 pages, 3 figs, 2 tables. A section with new results has been added. Revised version accepted for pubblication on Journal of Fluid Mechanics

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