Vortex formation in Daphnia swarms

We propose a self-propelled particle model for the swarming of Daphnia, which takes into account propulsion of the particles, mutual avoidance of close encounters and attraction to a center. Various key parameters are identified in order to arrive at a phase diagram for qualitatively different steady-state motions. We find that a vertex is formed only in a finite range of propulsions, and analyze its transitions to other states. Hydrodynamic interaction between the particles can stabilize the vortex and change its velocity profile.