  Understanding the dynamics of material objects advected by turbulent flows is
a long standing question in fluid dynamics. In this perspective article we
focus on the characterization of the statistical properties of non-interacting
finite-sized massive spherical particles advected by a vigorous turbulent flow.
We study the fluctuations and temporal correlations of particle accelerations
and explore their behaviours with respect to the particle size and the particle
mass density by means of fully-resolved numerical simulations. We observe that
the measured trends can not be interpreted as the simple multiplicative
combination of the two dominant effects: the spatial filtering of fluid
accelerations and the added-mass-adjusted fluid-to-particle density ratio. We
argue that other hydrodynamical forces or effects, e.g. preferential flow
sampling, have still a significant role even at the largest particle sizes,
which rich here the integral scale of turbulence.
