  Cellular suspensions such as dense bacterial flows exhibit a turbulence-like
phase under certain conditions. We study this phenomenon of "active turbulence"
statistically by using numerical tools. Following Wensink et al. [Proc. Natl.
Acad. Sci. U.S.A. 109, 14308 (2012)], we model active turbulence by means of a
generalized Navier-Stokes equation. Two-point velocity statistics of active
turbulence, both in the Eulerian and the Lagrangian frame, is explored. We
characterize the scale-dependent features of two-point statistics in this
system. Furthermore, we extend this statistical study with measurements of
vortex dynamics in this system. Our observations suggest that the large-scale
statistics of active turbulence is close to Gaussian with sub-Gaussian tails.
