  The distribution of particle accelerations in turbulence is intermittent,
with non-Gaussian tails that are quite different for light and heavy particles.
In this article we analyse a closure scheme for the acceleration fluctuations
of light and heavy inertial particles in turbulence, formulated in terms of
Lagrangian correlation functions of fluid tracers. We compute the variance and
the flatness of inertial particle accelerations and we discuss their dependency
on the Stokes number. The closure incorporates effects induced by the
Lagrangian correlations along the trajectories of fluid tracers, and its
predictions agree well with results of direct numerical simulations of inertial
particles in turbulence, provided that the effects induced by the inertial
preferential sampling of heavy/light particles outside/inside vortices are
negligible. In particular, the scheme predicts the correct functional behaviour
of the acceleration variance, as a function of Stokes, as well as the presence
of a minimum/maximum for the flatness of the acceleration of heavy/light
particles, in good qualitative agreement with numerical data. We also show that
the closure works well when applied to the Lagrangian evolution of particles
using a stochastic surrogate for the underlying Eulerian velocity field. Our
results support the conclusion that there exist important contributions to the
statistics of the acceleration of inertial particles independent of the
preferential sampling. For heavy particles we observe deviations between the
predictions of the closure scheme and direct numerical simulations, at Stokes
numbers of order unity. For light particles the deviation occurs for larger
Stokes numbers.
