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Meso-scale turbulence was originally observed experimentally in varioussuspensions of swimming bacteria, as well as in the collective motion of activecolloids. The corresponding large-scale dynamical patterns were reproduced in asimple model of a polar fluid, assuming a constant density of active particles.Recent, more detailed experimental studies revealed additional interestingaspects, such as anomalous velocity statistics and clustering phenomena. Thosephenomena cannot be explained by currently available models for active polarfluids. Herein, we extend the continuum model suggested by Dunkel et al. toinclude density variations and a feedback between the local density andself-propulsion speed of the active particles. If the velocity decreases strongenough with the density, a linear stability analysis of the resulting modelshows that, in addition to the short-wavelength instability of the originalmodel, a long-wavelength instability occurs. This is typically observed forhigh densities of polar active particles and is analogous to the well-knownphenomenon of motility-induced phase separation (MIPS) in scalar active matter.We determine a simple phase diagram indicating the linear instabilities andperform systematic numerical simulations for the various regions in thecorresponding parameter space. The interplay between the well understoodshort-range instability and the long-range instability leads to interestingdynamics and novel phenomena concerning nucleation and coarsening processes.Our simulation results display a rich variety of novel patterns, includingphase separation into domains with dynamically changing irregularly shapedboundaries. Anomalous velocity statistics are observed in all phases where thesystem segregates into regions of high and low densities. This offers a simpleexplanation for their occurrence in recent experiments with bacterialsuspensions.

Motility-Induced Clustering and Meso-Scale Turbulence in Active Polar Fluids