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Topological properties of physical systems play a crucial role in ourunderstanding 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 ofLagrangian trajectories depends on the mean helicity. Thus, a globaltopological invariant and a topological number of fluid trajectories becomerelated, and we provide an empirical expression linking them. The relationshows the existence of long-term memory in the trajectories: the links can bemade of the trajectory up to a given time, with particles positions in thepast. This property also allows experimental measurements of mean helicity.

Broken mirror symmetry of tracer's trajectories in turbulence