Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence
Abstract
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 Str <<1, 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 Str≳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 velocitymore »
- Authors:
-
- 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
- Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering
- Publication Date:
- Research Org.:
- Cornell Univ., Ithaca, NY (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)
- Contributing Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- OSTI Identifier:
- 1329877
- Report Number(s):
- LA-UR-15-24949
Journal ID: ISSN 1539-3755
- Grant/Contract Number:
- CBET-0967349
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 2; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
Citation Formats
Bragg, Andrew D., Ireland, Peter J., and Collins, Lance R. Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.92.023029.
Bragg, Andrew D., Ireland, Peter J., & Collins, Lance R. Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. United States. https://doi.org/10.1103/PhysRevE.92.023029
Bragg, Andrew D., Ireland, Peter J., and Collins, Lance R. 2015.
"Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence". United States. https://doi.org/10.1103/PhysRevE.92.023029. https://www.osti.gov/servlets/purl/1329877.
@article{osti_1329877,
title = {Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence},
author = {Bragg, Andrew D. and Ireland, Peter J. and Collins, Lance R.},
abstractNote = {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 Str <<1, 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 Str≳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 Str<<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 Str<<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.},
doi = {10.1103/PhysRevE.92.023029},
url = {https://www.osti.gov/biblio/1329877},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
issn = {1539-3755},
number = 2,
volume = 92,
place = {United States},
year = {Thu Aug 27 00:00:00 EDT 2015},
month = {Thu Aug 27 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation
journal, January 2009
- Ishihara, Takashi; Gotoh, Toshiyuki; Kaneda, Yukio
- Annual Review of Fluid Mechanics, Vol. 41, Issue 1
On Lagrangian single-particle statistics
journal, May 2012
- Falkovich, Gregory; Xu, Haitao; Pumir, Alain
- Physics of Fluids, Vol. 24, Issue 5
Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence
journal, November 2007
- Zaichik, Leonid I.; Alipchenkov, Vladimir M.
- Physics of Fluids, Vol. 19, Issue 11
Acceleration-based classification and evolution of fluid flow structures in two-dimensional turbulence
journal, August 2010
- Faber, Tristan; Vassilicos, J. C.
- Physical Review E, Vol. 82, Issue 2
Effect of Mixing on the Nucleation and Growth of Titania Particles
journal, May 2003
- Moody, Eric G.; Collins, Lance R.
- Aerosol Science and Technology, Vol. 37, Issue 5
New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles
journal, May 2014
- Bragg, Andrew D.; Collins, Lance R.
- New Journal of Physics, Vol. 16, Issue 5
New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities
journal, May 2014
- Bragg, Andrew D.; Collins, Lance R.
- New Journal of Physics, Vol. 16, Issue 5
Rapid planetesimal formation in turbulent circumstellar disks
journal, August 2007
- Johansen, Anders; Oishi, Jeffrey S.; Low, Mordecai-Mark Mac
- Nature, Vol. 448, Issue 7157
On the universality of the Kolmogorov constant
journal, November 1995
- Sreenivasan, Katepalli R.
- Physics of Fluids, Vol. 7, Issue 11
Stochastic suspensions of heavy particles
journal, August 2008
- Bec, Jérémie; Cencini, Massimo; Hillerbrand, Rafaela
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Turbulent Clustering of Protoplanetary dust and Planetesimal Formation
journal, September 2011
- Pan, Liubin; Padoan, Paolo; Scalo, John
- The Astrophysical Journal, Vol. 740, Issue 1
Spray combustion phenomena
journal, January 1996
- Faeth, G. M.
- Symposium (International) on Combustion, Vol. 26, Issue 1
Pair dispersion and preferential concentration of particles in isotropic turbulence
journal, January 2003
- Zaichik, Leonid I.; Alipchenkov, Vladimir M.
- Physics of Fluids, Vol. 15, Issue 6
Aerodynamics and aerosol particle deaggregation phenomena in model oral-pharyngeal cavities
journal, December 1996
- Li, Wen-I; Perzl, Michael; Heyder, Joachim
- Journal of Aerosol Science, Vol. 27, Issue 8
Inertial particle relative velocity statistics in homogeneous isotropic turbulence
journal, March 2012
- Salazar, Juan P. L. C.; Collins, Lance R.
- Journal of Fluid Mechanics, Vol. 696
Lagrangian evolution of velocity increments in rotating turbulence: The effects of rotation on non-Gaussian statistics
journal, October 2010
- Li, Yi
- Physica D: Nonlinear Phenomena, Vol. 239, Issue 20-22
Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence
journal, November 2006
- Goto, Susumu; Vassilicos, J. C.
- Physics of Fluids, Vol. 18, Issue 11
Statistical models for predicting pair dispersion and particle clustering in isotropic turbulence and their applications
journal, October 2009
- Zaichik, Leonid I.; Alipchenkov, Vladimir M.
- New Journal of Physics, Vol. 11, Issue 10
Ergodic and non-ergodic clustering of inertial particles
journal, December 2011
- Gustavsson, K.; Mehlig, B.
- EPL (Europhysics Letters), Vol. 96, Issue 6
On the two‐way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification
journal, July 1993
- Elghobashi, S.; Truesdell, G. C.
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 7
Symmetries of the turbulent state
journal, February 2009
- Falkovich, Gregory
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 12
A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence
journal, November 2009
- Coleman, S. W.; Vassilicos, J. C.
- Physics of Fluids, Vol. 21, Issue 11
On the spatial distribution and nearest neighbor distance between particles in the water column determined from in situ holographic measurements
journal, February 2006
- Malkiel, E.; Abras, J. N.; Widder, E. A.
- Journal of Plankton Research, Vol. 28, Issue 2
Equation of motion for a small rigid sphere in a nonuniform flow
journal, January 1983
- Maxey, Martin R.
- Physics of Fluids, Vol. 26, Issue 4
The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields
journal, January 1987
- Maxey, M. R.
- Journal of Fluid Mechanics, Vol. 174
Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence
journal, November 1993
- Wang, Lian-Ping; Maxey, Martin R.
- Journal of Fluid Mechanics, Vol. 256
A numerical study of the modulation of isotropic turbulence by suspended particles
journal, January 1999
- Sundaram, Shivshankar; Collins, Lance R.
- Journal of Fluid Mechanics, Vol. 379
Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations
journal, March 1997
- Sundaram, Shivshankar; Collins, Lance R.
- Journal of Fluid Mechanics, Vol. 335
Statistical mechanical description and modelling of turbulent collision of inertial particles
journal, July 2000
- Wang, Lian-Ping; Wexler, Anthony S.; Zhou, Yong
- Journal of Fluid Mechanics, Vol. 415
Clustering of aerosol particles in isotropic turbulence
journal, July 2005
- Chun, Jaehun; Koch, Donald L.; Rani, Sarma L.
- Journal of Fluid Mechanics, Vol. 536
Heavy Particle Concentration in Turbulence at Dissipative and Inertial Scales
journal, February 2007
- Bec, J.; Biferale, L.; Cencini, M.
- Physical Review Letters, Vol. 98, Issue 8
Turbulent clustering of stagnation points and inertial particles
journal, April 2006
- Chen, L.; Goto, S.; Vassilicos, J. C.
- Journal of Fluid Mechanics, Vol. 553, Issue -1
Transport Properties of Saturated and Unsaturated Porous Fractal Materials
journal, January 2008
- Coleman, S. W.; Vassilicos, J. C.
- Physical Review Letters, Vol. 100, Issue 3
Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence
journal, November 2005
- Naso, Aurore; Pumir, Alain
- Physical Review E, Vol. 72, Issue 5
Origin of Non-Gaussian Statistics in Hydrodynamic Turbulence
journal, October 2005
- Li, Yi; Meneveau, Charles
- Physical Review Letters, Vol. 95, Issue 16
Intermittent Distribution of Inertial Particles in Turbulent Flows
journal, March 2001
- Balkovsky, E.; Falkovich, G.; Fouxon, A.
- Physical Review Letters, Vol. 86, Issue 13
Intermittent Distribution of Inertial Particles in Turbulent Flows
text, January 2001
- Balkovsky, E.; Falkovich, G.; Fouxon, A.
- The American Physical Society
Rapid planetesimal formation in turbulent circumstellar discs
text, January 2007
- Johansen, Anders; Oishi, Jeffrey S.; Mac Low, Mordecai-Mark
- arXiv
Ergodic and non-ergodic clustering of inertial particles
text, January 2011
- Gustavsson, K.; Mehlig, B.
- arXiv
Works referencing / citing this record:
Particle-pair relative velocity measurement in high-Reynolds-number homogeneous and isotropic turbulence using 4-frame particle tracking velocimetry
journal, January 2018
- Dou, Zhongwang; Ireland, Peter J.; Bragg, Andrew D.
- Experiments in Fluids, Vol. 59, Issue 2
Statistical models for spatial patterns of heavy particles in turbulence
journal, January 2016
- Gustavsson, K.; Mehlig, B.
- Advances in Physics, Vol. 65, Issue 1
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects
journal, May 2016
- Ireland, Peter J.; Bragg, Andrew D.; Collins, Lance R.
- Journal of Fluid Mechanics, Vol. 796
A model study of the effect of clustering on the last stage of drizzle formation
journal, October 2019
- Madival, Deepak G.
- Quarterly Journal of the Royal Meteorological Society, Vol. 145, Issue 725
Particles in turbulent separated flow over a bump: Effect of the Stokes number and lift force
journal, October 2019
- Mollicone, J. -P.; Sharifi, M.; Battista, F.
- Physics of Fluids, Vol. 31, Issue 10
Clustering of heavy particles in vortical flows: a selective review
journal, March 2017
- Ravichandran, S.; Deepu, P.; Govindarajan, Rama
- Sādhanā, Vol. 42, Issue 4
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects
journal, May 2016
- Ireland, Peter J.; Bragg, Andrew D.; Collins, Lance R.
- Journal of Fluid Mechanics, Vol. 796
Statistical models for spatial patterns of heavy particles in turbulence
text, January 2014
- Gustavsson, K.; Mehlig, B.
- arXiv
Particle-Pair Relative Velocity Measurement in High-Reynolds-Number Homogeneous and Isotropic Turbulence Using 4-Frame Particle Tracking Velocimetry
text, January 2017
- Dou, Zhongwang; Ireland, Peter J.; Bragg, Andrew D.
- arXiv