  We present high-resolution direct numerical simulations of turbulent
three-dimensional Rayleigh-Benard convection with a focus on the Lagrangian
properties of the flow. The volume is a Cartesian slab with an aspect ratio of
four bounded by free-slip planes at the top and bottom and with periodic side
walls. The turbulence is inhomogeneous with respect to the vertical direction.
This manifests in different lateral and vertical two-particle dispersion and in
a dependence of the dispersion on the initial tracer position for short and
intermediate times. Similar to homogeneous isotropic turbulence, the dispersion
properties depend in addition on the initial pair separation and yield a
short-range Richardson-like scaling regime of two-particle dispersion for
initial separations close to the Kolmogorov dissipation length. The Richardson
constant is about half the value of homogeneous isotropic turbulence. The
multiparticle statistics is very close to the homogeneous isotropic case.
Clusters of four Lagrangian tracers show a clear trend to form flat, almost
coplanar objects in the long-time limit and deviate from the Gaussian
prediction. Significant efforts have been taken to resolve the statistics of
the acceleration components up to order four correctly. We find that the
vertical acceleration is less intermittent than the lateral one. The joint
statistics of the vertical acceleration with the local convective and
conductive heat flux suggests that rising and falling thermal plumes are not
associated with the largest acceleration magnitudes. It turns out also that the
Nusselt number which is calculated in the Lagrangian frame converges slowly in
time to the standard Eulerian one.
