  A universal characteristic of mesoscale turbulence in active suspensions is
the emergence of a typical vortex length scale, distinctly different from the
scale-invariance of turbulent high-Reynolds number flows. Collective
length-scale selection has been observed in bacterial fluids, endothelial
tissue and active colloides, yet the physical origins of this phenomenon remain
elusive. Here, we systematically derive an effective fourth-order field theory
from a generic microscopic model that allows us to predict the typical vortex
size in microswimmer suspensions. Building on a self-consistent closure
condition, the derivation shows that the vortex length scale is determined by
the competition between local alignment forces and intermediate-range
hydrodynamic interactions. Vortex structures found in simulations of the theory
agree with recent measurements in Bacillus subtilis suspensions. Moreover, our
approach correctly predicts an effective viscosity enhancement (reduction), as
reported experimentally for puller (pusher) microorganisms.
