  We define and characterize multi-time Lagrangian structure functions using
data stemming from two swirling flows with mean flow and turbulent
fluctuations: A Taylor-Green numerical flow, and a von K\'arm\'an laboratory
experiment. Data is obtained from numerical integration of tracers in the
former case, and from three-dimensional particle tracking velocimetry
measurements in the latter. Multi-time statistics are shown to decrease the
contamination of large scales in the inertial range scaling. A time scale at
which contamination from the mean flow becomes dominant is identified, with
this scale separating two different Lagrangian scaling ranges. The results from
the multi-time structure functions also indicate that Lagrangian intermittency
is not a result of large-scale flow effects. The multi-time Lagrangian
structure functions can be used without prior knowledge of the forcing
mechanisms or boundary conditions, allowing their application in different flow
geometries.
