Stability of metric and topological flocking models under flow

Aggregation of living organisms (as in, e.g., bird flocks, fish schools, insect swarms) is one of the most spectacular manifestations of self-organisation in Nature, with crucial implications for evolutionary biology, ecology and robotics. Agent-based models with simple social interaction rules have proven successful in reproducing some properties of flocking. Despite in most of these systems the individuals move in complex fluid environments, the role of the underlying fluid motion has been so far greatly overlooked. We simulate numerically metric (distance-based) and topological (nearest-neighbours based) flocking models of Lagrangian point-like particles performing autonomous motion and advected by vortical flows (stationary and oscillatory Taylor-Green vortex). We study the transition to flocking and the distribution of cluster sizes at changing the ratio of particle proper velocity and fluid reference velocity. We find that clusters emerge more easily in the metric model, but the topological one shows a greater tendency to form a single, large, flock. Moreover, we observe that the presence/absence of fluid flow selects a specific number of nearest neighbours within the topological approach. Finally, the stability of an initiliased cluster is addressed.