  Geophysical flows are often turbulent and subject to rotation. This rotation
modifies the structure of turbulence and is thereby expected to sensibly affect
its Lagrangian properties. Here, we investigate the relative dispersion and
geometry of pairs, triads and tetrads in homogeneous rotating turbulence, by
using direct numerical simulations at different rotation rates. Pair dispersion
is shown to be faster in the vertical direction (along the rotation axis) than
in the horizontal one. At long times, in Taylor's regime, this is due to the
slower decorrelation of the vertical velocity component as compared to the
horizontal one. At short times, in the ballistic regime, this result can be
interpreted by considering pairs of different orientations at the release time,
and is a signature of the anisotropy of Eulerian second-order functions.
Rotation also enhances the distortion of triads and tetrads also present in
homogeneous and isotropic turbulence. In particular, at long times, the
flattening of tetrads increases with the rotation rate. The maximal dimension
of triads and tetrads is shown to be preferentially aligned with the rotation
axis, in agreement with our observations for pairs.
