Weak-strong clustering transition in renewing compressible flows

TL;DR

This paper studies how the clustering of tracers in compressible flows depends on flow correlation, revealing a transition influenced by flow time scales and non-universal clustering behavior.

Contribution

It uncovers the dependence of clustering transition on flow correlation time and the non-universality of clustering properties in time-correlated compressible flows.

Findings

Critical compressibility minimizes when flow correlation time matches eddy turnover time.

Clustering properties are strongly influenced by the spatio-temporal structure of the velocity field.

Clustering transition depends on flow correlation, affecting tracer distribution patterns.

Abstract

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.