  Flagellated bacteria on nutrient-rich substrates can differentiate into a
swarming state and move in dense swarms across surfaces. A recent experiment
measured the flow in the fluid around an Escherichia coli swarm (Wu, Hosu and
Berg, 2011 Proc. Natl. Acad. Sci. USA 108 4147). A systematic chiral flow was
observed in the clockwise direction (when viewed from above) ahead of the swarm
with flow speeds of about $10~\mu$m/s, about 3 times greater than the radial
velocity at the edge of the swarm. The working hypothesis is that this flow is
due to the action of cells stalled at the edge of a colony that extend their
flagellar filaments outwards, moving fluid over the virgin agar. In this work
we quantitatively test his hypothesis. We first build an analytical model of
the flow induced by a single flagellum in a thin film and then use the model,
and its extension to multiple flagella, to compare with experimental
measurements. The results we obtain are in agreement with the flagellar
hypothesis. The model provides further quantitative insight into the flagella
orientations and their spatial distributions as well as the tangential speed
profile. In particular, the model suggests that flagella are on average
pointing radially out of the swarm and are not wrapped tangentially.
