Motility-induced clustering and meso-scale turbulence in active polar fluids

Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed studies in a variety of experimental realizations of active polar fluids revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested by Dunkel et al to include density variations and a local feedback between the local density and self-propulsion speed of the active polar particles. If the velocity decreases strong enough with the density, a linear stability analysis of the resulting model shows that, in addition to the short-wavelength instability of the original model, a long-wavelength instability occurs. This is typically observed for high densities of polar active particles and is analogous to the well-known phenomenon of motility-induced phase separation (MIPS) in scalar active matter. We determine a simple phase diagram indicating the linear instabilities and perform systematic numerical simulations for the various regions in the corresponding parameter space. The interplay between the well understood short-range instability (leading to meso-scale turbulence) and the long-range instability (associated with MIPS) leads to interesting dynamics and novel phenomena concerning nucleation and coarsening processes. Our simulation results display a rich variety of novel patterns, including phase separation into domains with dynamically changing irregularly shaped boundaries. Anomalous velocity statistics are observed in all phases where the system segregates into regions of high and low densities. This offers a simple explanation for their occurrence in recent experiments with bacterial suspensions.