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

Journal Article · Thu Aug 27 00:00:00 EDT 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.92.023029· OSTI ID:1329877

Bragg, Andrew D. ^[1]; Ireland, Peter J. ^[2]; Collins, Lance R. ^[2]

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1. Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering; Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Applied Mathematics and Plasma Physics Group
2. Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering

In this study, 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 St_r <<1, where St_r 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 St_r≳O(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. 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. 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 St_r<<1 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 and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for St_r<<1, which, unlike that in the dissipation range, is not scale invariant. Finally, the results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.

• Research Organization: Cornell Univ., Ithaca, NY (United States)
• Sponsoring Organization: USDOE; National Science Foundation (NSF)
• Contributing Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Grant/Contract Number: CBET-0967349
• OSTI ID: 1329877
• Report Number(s): LA-UR-15-24949
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, Issue 2; ISSN 1539-3755
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Mathematics