around a volume fraction of bacterial bodies of about $1-2\%$. At such densities, the typical distance between the organisms is about $5-8$ times their body length, collisions are rare, and the far-field hydrodynamic interactions are thought to be dominant [@Koch2011; @Saintillan2013]. The latter are well-described by a “pusher”-like Stokesian dipolar field [@Lauga2009; @Drescher2011], generated when two point forces of equal magnitude and pointing away from each other are applied to a viscous fluid. Self-propelled pusher-like dipolar particles thus form a minimal model for dilute bacterial suspensions.

The transition to collective motion in dilute bacterial suspensions can be understood in terms of a mean-field kinetic theory [@Koch2011; @Saintillan2013] incorporating the minimal ingredients discussed above. Such theory identifies re-orientation of bacteria in the velocity field created by other organisms as the key ingredient leading to a global isotropic-nematic transition. The globally ordered state is, however, linearly unstable through a long-wavelength generic instability [@AditiSimha2002; @Marchetti2013], and there ensue never-settling dynamics as a compromise between the two instabilities. The critical density of bacteria at the onset of collective motion is determined by the strength of their dipolar interactions, their shape, and the way individual organisms change their orientation: either by occasionally re-orienting in a 