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Flocking behavior is observed in biological systems from the cellular tosuper-organismal length scales, and the mechanisms and purposes of thisbehavior are objects of intense interest. In this paper, we study thecollective dynamics of bovine sperm cells in a viscoelastic fluid. Remarkably,these cells appear not to spontaneously flock, but transition into a long-livedflocking phase after being exposed to a transient ordering pulse of fluid flow.Surprisingly, this induced flocking phase exhibits anisotropic giant numberfluctuations and possesses transverse density fluctuation correlationsconsistent with the Toner-Tu theory of the polar fluid phase, despite theclearly important role of momentum conservation between the swimmers and thesurrounding fluid in these experiments. In addition to these flow-inducedflocking states, we also find a self-organized global vortex state of the spermcells. We simulate this system, modeling the sperm as persistently turningactive particles. Although the model does not reproduce the vortex state, itexhibits a polar-disorder phase boundary as a function of cell density andpersistence time that is predictive of the experimental phase boundary. Ourresults may have implications for the evaluation of sample fertility bystudying the collective phase behavior of dense groups of swimming sperm.

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells