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Weak–strong clustering transition in renewing compressible flows

Published online by Cambridge University Press:  25 November 2014

Ajinkya Dhanagare ,
Stefano Musacchio  and
Dario Vincenzi
Ajinkya Dhanagare
Affiliation:
Laboratoire J. A. Dieudonné, CNRS, Université Nice Sophia Antipolis, 06100 Nice, France
Stefano Musacchio
Affiliation:
Laboratoire J. A. Dieudonné, CNRS, Université Nice Sophia Antipolis, 06100 Nice, France
Dario Vincenzi*
Affiliation:
Laboratoire J. A. Dieudonné, CNRS, Université Nice Sophia Antipolis, 06100 Nice, France
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Mixing: Chaotic advection Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 431 - 442
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© 2014 Cambridge University Press 

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