Lattice model of bacterial turbulence

One of the most striking difference between active and passive systems is the appearance of collective motion in self-propelled particles suspended in a fluid observed in recent experiments and simulations: at low densities particles move around in an uncorrelated fashion, while at higher densities they organise into jets and vortices comprising many
individual swimmers. Recent work (Stenhammar et al, PRL 119, 028005 (2017)) suggests
that this transition is caused by mutual reorientation of the swimmers and is insensitive
to their translational degrees of freedom.

In this work we use this observation to propose a lattice-based model of collective motion.
We consider dipolar swimmers pinned to lattices of various symmetries, and study their
dynamics in the presence of long-ranged hydrodynamic interactions. We observe that in the absence of orientational noise or random reorientation, two-dimensional systems quickly reach steady-states, while three-dimensional lattices sustain continues dynamics. Our results suggest a fundamental difference between two- and three-dimensional bacterial turbulence.