  We investigate the statistical properties of Lagrangian tracers transported
by a time-correlated compressible renewing flow. We show that the preferential
sampling of the phase space performed by tracers yields significant differences
between the Lagrangian statistics and its Eulerian counterpart. In particular,
the effective compressibility experienced by tracers has a non-trivial
dependence on the time correlation of the flow. We examine the consequence of
this phenomenon on the clustering of tracers, focusing on the transition from
the weak- to the strong-clustering regime. We find that the critical
compressibility at which the transition occurs is minimum when the time
correlation of the flow is of the order of the typical eddy turnover time.
Further, we demonstrate that the clustering properties in time-correlated
compressible flows are non-universal and are strongly influenced by the
spatio-temporal structure of the velocity field.
