  Topological properties of physical systems play a crucial role in our
understanding of nature, yet their experimental determination remains elusive.
We show that the mean helicity, a dynamical invariant in ideal flows,
quantitatively affects trajectories of fluid elements: the linking number of
Lagrangian trajectories depends on the mean helicity. Thus, a global
topological invariant and a topological number of fluid trajectories become
related, and we provide an empirical expression linking them. The relation
shows the existence of long-term memory in the trajectories: the links can be
made of the trajectory up to a given time, with particles positions in the
past. This property also allows experimental measurements of mean helicity.
