  In dilute suspensions of swimming microorganisms the local fluid velocity is
a random superposition of the flow fields set up by the individual organisms,
which in turn have multipole contributions decaying as inverse powers of
distance from the organism. Here we show that the conditions under which the
central limit theorem guarantees a Gaussian probability distribution function
of velocities are satisfied when the leading force singularity is a Stokeslet,
but are not when it is any higher multipole. These results are confirmed by
numerical studies and by experiments on suspensions of the alga Volvox carteri,
which show that deviations from Gaussianity arise from near-field effects.
