Acceleration statistics of heavy particles in turbulence

We study, by means of direct numerical simulations, the dynamics 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 will show that the root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers, that at a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers and that the tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: particle clustering, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$.