The collective motion of microswimmers in suspensions induce patterns of
vortices on scales that are much larger than the characteristic size of a
microswimmer, attaining a state called bacterial turbulence. Hydrodynamic
turbulence acts on even larger scales and is dominated by inertial transport of
energy. Using an established modification of the Navier-Stokes equation that
accounts for the small scale forcing of hydrodynamic flow by microswimmers, we
study the properties of a dense supensions of microswimmers in two dimensions,
where the conservation of enstrophy can drive an inverse cascade through which
energy is accumulated on the largest scales. We find that the dynamical and
statistical properties of the flow show a sharp transition to the formation of
vortices at the largest length scale. The results show that 2d bacterial and
hydrodynamic turbulence are separated by a subcritical phase transition.Comment: postprint versio
