  Low Reynolds number direct simulations of large populations of
hydrodynamically interacting swimming particles confined between planar walls
are performed. The results of simulations are compared with a theory that
describes dilute suspensions of swimmers. The theory yields scalings with
concentration for diffusivities and velocity fluctuations as well as a
prediction of the fluid velocity spatial autocorrelation function. Even for
uncorrelated swimmers, the theory predicts anticorrelations between nearby
fluid elements that correspond to vortex-like swirling motions in the fluid
with length scale set by the size of a swimmer and the slit height. Very
similar results arise from the full simulations indicating either that
correlated motion of the swimmers is not significant at the concentrations
considered or that the fluid phase autocorrelation is not a sensitive measure
of the correlated motion. This result is in stark contrast with results from
unconfined systems, for which the fluid autocorrelation captures large-scale
collective fluid structures. The additional length scale (screening length)
introduced by the confinement seems to prevent these large-scale structures
from forming.
