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Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence

Publication ,  Journal Article
Bragg, AD; Ireland, PJ; Collins, LR
Published in: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
August 27, 2015

In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When StrO(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)NJOPFM1367-263010.1088/1367-2630/16/5/055013]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)PHFLE61070-663110.1063/1.3257638]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)PHFLE61070-663110.1063/1.2813044] and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for Str1, which, unlike that in the dissipation range, is not scale invariant. The results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.

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Published In

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

August 27, 2015

Volume

92

Issue

2

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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Bragg, A. D., Ireland, P. J., & Collins, L. R. (2015). Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92(2). https://doi.org/10.1103/PhysRevE.92.023029
Bragg, A. D., P. J. Ireland, and L. R. Collins. “Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 92, no. 2 (August 27, 2015). https://doi.org/10.1103/PhysRevE.92.023029.
Bragg AD, Ireland PJ, Collins LR. Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015 Aug 27;92(2).
Bragg, A. D., et al. “Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 92, no. 2, Aug. 2015. Scopus, doi:10.1103/PhysRevE.92.023029.
Bragg AD, Ireland PJ, Collins LR. Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015 Aug 27;92(2).

Published In

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

August 27, 2015

Volume

92

Issue

2

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences