  Swimming cells and microorganisms are as diverse in their collective dynamics
as they are in their individual shapes and propulsion mechanisms. Even for
sperm cells, which have a stereotyped shape consisting of a cell body connected
to a flexible flagellum, a wide range of collective dynamics is observed
spanning from the formation of tightly packed groups to the display of
larger-scale, turbulence-like motion. Using a detailed mathematical model that
resolves flagellum dynamics, we perform simulations of sperm suspensions
containing up to 1000 cells and explore the connection between individual and
collective dynamics. We find that depending on the level of variation in
individual dynamics from one swimmer to another, the sperm exhibit either a
strong tendency to aggregate, or the suspension exhibits large-scale swirling.
Hydrodynamic interactions govern the formation and evolution of both states. In
addition, a quantitative analysis of the states reveals that the flows
generated at the time-scale of flagellum undulations contribute significantly
to the overall energy in the surrounding fluid, highlighting the importance of
resolving these flows.
