  We explore the velocity fluctuations in a fluid due to a dilute suspension of
randomly-distributed vortex rings at moderate Reynolds number, for instance
those generated by a large colony of jellyfish. Unlike previous analysis of
velocity fluctuations associated with gravitational sedimentation or
suspensions of microswimmers, here the vortices have a finite lifetime and are
constantly being produced. We find that the net velocity distribution is
similar to that of a single vortex, except for the smallest velocities which
involve contributions from many distant vortices; the result is a truncated
$5/3$-stable distribution with variance (and mean energy) linear in the vortex
volume fraction $\phi$. The distribution has an inner core with a width scaling
as $\phi^{3/5}$, then long tails with power law $|u|^{-8/3}$, and finally a
fixed cutoff (independent of $\phi$) above which the probability density scales
as $|u|^{-5}$, where $u$ is a component of the velocity. We argue that this
distribution is robust in the sense that the distribution of any velocity
fluctuations caused by random forces localized in space and time has the same
properties, except possibly for a different scaling after the cutoff.
