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We investigate the statistical properties of Lagrangian tracers transportedby a time-correlated compressible renewing flow. We show that the preferentialsampling of the phase space performed by tracers yields significant differencesbetween the Lagrangian statistics and its Eulerian counterpart. In particular,the effective compressibility experienced by tracers has a non-trivialdependence on the time correlation of the flow. We examine the consequence ofthis phenomenon on the clustering of tracers, focusing on the transition fromthe weak- to the strong-clustering regime. We find that the criticalcompressibility at which the transition occurs is minimum when the timecorrelation of the flow is of the order of the typical eddy turnover time.Further, we demonstrate that the clustering properties in time-correlatedcompressible flows are non-universal and are strongly influenced by thespatio-temporal structure of the velocity field.

Weak-strong clustering transition in renewing compressible flows