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Some Aspects of the Collective Dynamics of Particles in Turbulent Flows

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Collective Dynamics of Particles

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 576))

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Abstract

This chapter presents some important features of collective dynamics of particles transported by a turbulent flow. The focus is on two main processes. The first concerns the dispersion of fluid tracers (i.e. particles which follow exactly the flow) and revisits the classical problem of turbulent pair dispersion. It is shown, that a simple scale-dependent iterative ballistic process accurately accounts for most turbulent super-diffusive properties, which are explicitly related to the multi-scale nature of turbulence via the turbulent energy spectrum. The second considers the case of inertial particles (which are not tracers of the carrier flow) and the phenomenon of preferential concentration, responsible for the formation of persistent particle clusters. Tools to diagnose the presence of clustering are reviewed, together with the main properties of clusters in turbulence and of the underlying particles/turbulence interaction mechanisms.

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References

  • A Aliseda, A Cartellier, F Hainaux, and J C Lasheras. Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics, 468:77–105, 2002.

    Google Scholar 

  • Alfred Barnard Basset. A treatise on hydrodynamics, volume 2. Deighton, Bell and Co., 1888.

    Google Scholar 

  • G K Batchelor. The application of the similarity theory of turbulence to atmospheric diffusion. Quarterly Journal of the Royal Meteorological Sociey, 76(328):133–146, 1950. ISSN 0035-9009.

    Google Scholar 

  • G K Batchelor. Diffusion in a field of homogeneous turbulence II. The relative motion of particles. Proceedings of the Cambridge Philosophical Society, 48(2):345–362, 1952.

    Google Scholar 

  • Jeremie Bec, Luca Biferale, Massimo Cencini, Alessandra Lanotte, Stefano Musacchio, and Federico Toschi. Heavy particle concentration in turbulence at dissipative and inertial scales. Physical Review Letters, 98(8):84502, 2007. ISSN 0031-9007. doi:10.1103/PhysRevLett.98.084502. URL https://doi.org/10.1103/PhysRevLett.98.084502.

  • Jacob Berg, Beat Lüthi, Jakob Mann, and Sø ren Ott. Backwards and forwards relative dispersion in turbulent flow: An experimental investigation. Physical Review E, 74(1):016304, July 2006. ISSN 1539-3755. doi:10.1103/PhysRevE.74.016304. URL http://link.aps.org/doi/10.1103/PhysRevE.74.016304.

  • L Biferale, G Boffetta, A Celani, B J Devenish, A Lanotte, and F Toschi. Lagrangian statistics of particles pairs in homogeneous isotropic turbulence. Physics of Fluids, 17:115101, 2005.

    Google Scholar 

  • Rehab Bitane, Holger Homann, and Jérémie Bec. Time scales of turbulent relative dispersion. Physical Review E, 86(4):045302, October 2012. ISSN 1539-3755. doi:10.1103/PhysRevE.86.045302. URL http://link.aps.org/doi/10.1103/PhysRevE.86.045302.

  • G Boffetta and A Celani. Pair dispersion in turbulence. Physica A, 280(1-2):1–9, 2000. ISSN 0378-4371.

    Google Scholar 

  • G. Boffetta and I. Sokolov. Relative Dispersion in Fully Developed Turbulence: The Richardsons Law and Intermittency Corrections. Physical Review Letters, 88(9):094501, February 2002. ISSN 0031-9007. doi:10.1103/PhysRevLett.88.094501. URL http://link.aps.org/doi/10.1103/PhysRevLett.88.094501.

  • Mickael Bourgoin. Turbulent pair dispersion as a ballistic cascade phenomenology. Journal of Fluid Mechanics, 772:678–704, 2015.

    Google Scholar 

  • Mickaël Bourgoin and Haitao Xu. Focus on dynamics of particles in turbulence. New Journal of Physics, 16(8):085010, August 2014. ISSN 1367-2630. doi:10.1088/1367-2630/16/8/085010. URL http://stacks.iop.org/1367-2630/16/i=8/a=085010?key=crossref.963834ca83 607a6aa71791a4a68b0777.

  • Mickael Bourgoin, Nicholas T Ouellette, Haitao Xu, Jacob Berg, and Eberhard Bodenschatz. The role of pair dispersion in turbulent flow. Science, 311(5762):835–838, 2006. doi:10.1126/science.1121726.

  • Mickael Bourgoin, Jean-François Pinton, and Romain Volk. Lagrangian methods in experimental fluid mechanics. In Thomas von Larcher and Paul D. Williams, editors, Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations, page 360. John Wiley & Sons, Inc., 2014. ISBN 1118855930. URL https://books.google.com/books?hl=fr&lr=&id=8GezBQAAQBAJ&pgis=1.

  • Joseph Boussinesq. Th \(\{\) é \(\}\) orie analytique de la chaleur: mise en harmonie avec la thermodynamique et avec la th \(\{\) é \(\}\) orie m \(\{\) é \(\}\) canique de la lumi \(\{\) é \(\}\) re, volume 2. Gauthier-Villars, 1903.

    Google Scholar 

  • S W Coleman and J C Vassilicos. A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence. Physics of Fluids, 21(11):113301, November 2009. ISSN 1070–6631. doi:10.1063/1.3257638.

  • T. Faber and J. C. Vassilicos. Turbulent pair separation due to multiscale stagnation point structure and its time asymmetry in two-dimensional turbulence. Physics of Fluids, 21(1):015106, 2009. ISSN 10706631. doi:10.1063/1.3059618. URL http://scitation.aip.org/content/aip/journal/pof2/21/1/10.1063/1.305961 8.

  • Jarai-Szabo Ferenc and Zoltan Neda. On the size distribution of Poisson Voronoi cells. Physica A-Statistical Mechanics and Its Applications, 385(2):518–526, 2007. doi:10.1016/j.physa.2007.07.063.

  • Jr Fessler, Jd Kulick, and Jk Eaton. Preferential Concentration Of Heavy-Particles In A Turbulent Channel Flow. Physics of Fluids, 6(11):3742–3749, 1994.

    Google Scholar 

  • Renée Gatignol. The Faxen formulas for a rigid particle in an unsteady non-uniform Stoke flow. Journal de Mécanique Théorique et Appliquée, 2(2):143–160, 1983.

    Google Scholar 

  • Susumu Goto and J. Vassilicos. Sweep-Stick Mechanism of Heavy Particle Clustering in Fluid Turbulence. Physical Review Letters, 100(5):54503, February 2008. ISSN 0031-9007. doi:10.1103/PhysRevLett.100.054503. URL http://link.aps.org/doi/10.1103/PhysRevLett.100.054503.

  • M Huber, J C McWilliams, and M Ghil. A climatology of turbulent dispersion in the troposphere. Journal of the Atmospheric Sciences, 58(16):2377–2394, 2001.

    Google Scholar 

  • Jennifer Jucha, Haitao Xu, Alain Pumir, and Eberhard Bodenschatz. Time-reversal-symmetry Breaking in Turbulence. Physical Review Letters, 113(5):054501, July 2014. ISSN 0031-9007. doi:10.1103/PhysRevLett.113.054501. URL http://link.aps.org/doi/10.1103/PhysRevLett.113.054501.

  • J. Klafter, A. Blumen, and M. F. Shlesinger. Stochastic pathway to anomalous diffusion. Physical Review E, 35:3081–3085, 1987.

    Google Scholar 

  • A. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akacl. Nauk SSSR, 30:301–305, 1941. ISSN 0002-3264.

    Google Scholar 

  • Arthur LaPorta, Greg A Voth, Alice M Crawford, Jim Alexander, and Eberhard Bodenschatz. Fluid particle accelerations in fuly developped turbulence. Nature, 409:1017, 2001.

    Google Scholar 

  • J Mann, S Ott, and J S Andersen. Experimental study of relative, turbulent diffusion. Technical Report Riso-R-1036 (EN), Risoe National Laboratory, Roskilde, Denmark, 1999.

    Google Scholar 

  • M Maxey. The Gravitational Settling Of Aerosol-Particles In Homogeneous Turbulence And Random Flow-Fields. Journal of Fluid Mechanics, 174:441–465, 1987.

    Google Scholar 

  • Martin R Maxey and James J Riley. Equation of motion for a small rigid sphere in a nonuniform flow. Physics of Fluids, 26(4):883–889, 1983.

    Google Scholar 

  • B. Mehlig, M. Wilkinson, K. Duncan, T. Weber, and M. Ljunggren. Aggregation of inertial particles in random flows. Physical Review E, 72(5):051104, November 2005. ISSN 1539-3755. doi:10.1103/PhysRevE.72.051104. URL http://link.aps.org/doi/10.1103/PhysRevE.72.051104.

  • Bernhard Mehlig and Michael Wilkinson. Coagulation by Random Velocity Fields as a Kramers Problem. Physical Review Letters, 92(25):250602, June 2004. ISSN 0031-9007. doi:10.1103/PhysRevLett.92.250602. URL http://link.aps.org/doi/10.1103/PhysRevLett.92.250602.

  • R Monchaux, M Bourgoin, and A Cartellier. Preferential concentration of heavy particles: A Voronoi analysis. Physics of Fluids, 22(10):103304, 2010. doi:10.1063/1.3489987.

  • Romain Monchaux, Mickael Bourgoin, and Alain Cartellier. Analyzing preferential concentration and clustering of inertial particles in turbulence. International Journal of Multiphase Flow, 40:1–18, 2012. ISSN 0301-9322. doi:10.1016/j.ijmultiphaseflow.2011.12.001. URL http://www.sciencedirect.com/science/article/pii/S030193221100245X.

  • M NELKIN and R M KERR. DECAY OF SCALAR VARIANCE IN TERMS OF A MODIFIED RICHARDSON LAW FOR PAIR DISPERSION. Physics of Fluids, 24(9):1754–1756, 1981.

    Google Scholar 

  • Martin Obligado, Tomas Teitelbaum, Alain Cartellier, Pablo D. Mininni, and Mickael Bourgoin. Preferential Concentration of Heavy Particles in Turbulence. Journal of Turbulence, 15(5):293–310, 2014.

    Google Scholar 

  • Piero Olla. Preferential concentration versus clustering in inertial particle transport by random velocity fields. Physical Review E, 81(1):16305, January 2010. ISSN 1539-3755. doi:10.1103/PhysRevE.81.016305. URL http://link.aps.org/doi/10.1103/PhysRevE.81.016305.

  • Carl Wilhelm Oseen. \(\{\) Ü \(\}\) ber die Stoke’sche Formel und \(\{\) ü \(\}\) ber eine verwandte Aufgabe in der Hydrodynamik:... Almqvist & Wiksell, 1911.

    Google Scholar 

  • Soren Ott and Jakob Mann. An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. Journal of Fluid Mechanics, 422:207–223, 2000.

    Google Scholar 

  • Nicholas T Ouellette, Haitao Xu, Mickaël Bourgoin, and Eberhard Bodenschatz. An experimental study of turbulent relative dispersion models. New Journal of Physics, 8(6):109, June 2006. ISSN 1367-2630. doi:10.1088/1367-2630/8/6/109. URL http://stacks.iop.org/1367-2630/8/i=6/a=109?key=crossref.6c8e470b5e7116 e5021ffd8b32247aa7.

  • Lewis F Richardson. Atmospheric Diffusion Shown on a Distance-Neighbour Graph. Proceedings of the Royal Society of London, Series A, 110(756):709–737, 1926.

    Google Scholar 

  • Juan P L C Salazar and Lance R Collins. Two-Particle Dispersion in Isotropic Turbulent Flows. ANNUAL REVIEW OF FLUID MECHANICS, 41:405–432, 2009. ISSN 0066-4189. doi:10.1146/annurev.fluid.40.111406.102224.

  • Juan P L C Salazar, Jeremy de Jong, Lujie Cao, Scott H Woodward, Hui Meng, and Lance R Collins. Experimental and numerical investigation of inertial particle clustering in isotropic turbulence. Journal of Fluid Mechanics, 600(1):245–256, 2008. ISSN 0022-1120. doi:10.1017/S0022112008000372. URL http://journals.cambridge.org/production/action/cjoGetFulltext?fulltext id=1818596.

  • Ewe Wei Saw, Raymond A Shaw, Sathyanarayana Ayyalasomayajula, Patrick Y Chuang, and Armann Gylfason. Inertial clustering of particles in high-reynolds-number turbulence. Physical Review Letters, 100(21), 2008. ISSN 0031-9007. doi:10.1103/PhysRevLett.100.214501.

  • Brian Sawford. Turbulent Relative Dispersion. Annual Review of Fluid Mechanics, 33:289–317, 2001.

    Google Scholar 

  • Brian L. Sawford, P. K. Yeung, and Michael S. Borgas. Comparison of backwards and forwards relative dispersion in turbulence. Physics of Fluids, 17(9):095109, 2005. ISSN 10706631. doi:10.1063/1.2047593. URL http://scitation.aip.org/content/aip/journal/pof2/17/9/10.1063/1.204759 3.

  • Stephen J Scott, Aditya U Karnik, and John S Shrimpton. On the quantification of preferential accumulation. INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW, 30(4):789–795, 2009. ISSN 0142-727X. doi:10.1016/j.ijheatfluidflow.2009.02.002.

  • K D Squires and J K Eaton. Preferential concentration of particles by turbulence. Physics of Fluids A, 3(5):1169–1178, 1991.

    Google Scholar 

  • Katepalli R Sreenivasan. On the universality of the Kolmogorov constant. Physics of Fluids, 7(3):2778–2784, 1995.

    Google Scholar 

  • G I Taylor. Diffusion by continuous movements. Proc. Lond. Math. Soc., 20:196–212, 1922.

    Google Scholar 

  • Federico Toschi and Eberhard Bodenschatz. Lagrangian Properties of Particles in Turbulence. Annual Review of Fluid Mechanics, 41:375–404, 2009. doi:10.1146/annurev.fluid.010908.165210.

  • Greg A Voth, Arthur LaPorta, Alice M Crawford, Jim Alexander, and Eberhard Bodenschatz. Measurement of particle accelerations in fully developed turbulence. Journal of Fluid Mechanics, 469:121–160, 2002.

    Google Scholar 

  • A M Wood, W Hwang, and J K Eaton. Preferential concentration of particles in homogeneous and isotropic turbulence. International Journal of Multiphase Flow, 31:1220–1230, 2005.

    Google Scholar 

  • P K Yeung and S B Pope. Lagrangian statistics from direct numerical simulations of isotropic turbulence. Journal of Fluid Mechanics, 207:531–586, 1989.

    Google Scholar 

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Authors and Affiliations

  1. Physics Laboratory, Ecole Normale Superieure of Lyon, Lyon, France

    Mickaël Bourgoin

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  1. Mickaël Bourgoin
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Correspondence to Mickaël Bourgoin .

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  1. Department of Electrical, Management and Mechanical Engineering, University of Udine, Udine, Italy

    Cristian Marchioli

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Bourgoin, M. (2017). Some Aspects of the Collective Dynamics of Particles in Turbulent Flows. In: Marchioli, C. (eds) Collective Dynamics of Particles. CISM International Centre for Mechanical Sciences, vol 576. Springer, Cham. https://doi.org/10.1007/978-3-319-51226-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-51226-6_3

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