  The collective effects of microswimmers in active suspensions result in
active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is
characterized by the presence of vortices and jets at scales much larger than
the characteristic size of the individual active constituents. To describe this
dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces
have been proposed. Here, we provide a justification of such models for the
case of dense suspensions in two dimensions (2d). We subsequently carry out an
in-depth numerical study of the properties of one-fluid models as a function of
the active driving in view of possible transition scenarios from active
turbulence to large-scale pattern, referred to as condensate, formation induced
by the classical inverse energy cascade in Newtonian 2d turbulence. Using a
one-fluid model it was recently shown (Linkmann et al., Phys. Rev. Lett. (in
press)) that two-dimensional active suspensions support two non-equilibrium
steady states, one with a condensate and one without, which are separated by a
subcritical transition. Here, we report further details on this transition such
as hysteresis and discuss a low-dimensional model that describes the main
features of the transition through nonlocal-in-scale coupling between the
small-scale driving and the condensate.
