Environmental Fluid Mechanics

, Volume 7, Issue 2, pp 173–193 | Cite as

Clustering of aerosols in atmospheric turbulent flow

  • Tov ElperinEmail author
  • Nathan Kleeorin
  • Michael A. Liberman
  • Victor S. L’vov
  • Igor Rogachevskii
Original Article


A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of small-scale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.


Turbulent transport of aerosols and droplets Atmospheric turbulent flow Particle clustering instability 


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  1. 1.
    Monin AS, Yaglom AM (1975) Statistical fluid mechanics: mechanics of turbulence, vol 2. M.I.T. Press, CambridgeGoogle Scholar
  2. 2.
    Csanady GT (1980) Turbulent diffusion in the environment. Reidel, DordrechtGoogle Scholar
  3. 3.
    Pasquill F, Smith FB (1983) Atmospheric diffusion. Ellis Horwood, ChichesterGoogle Scholar
  4. 4.
    McComb WD (1990) The physics of fluid turbulence. Clarendon Press, OxfordGoogle Scholar
  5. 5.
    Stock D (1996) Particle dispersion in flowing gases. J Fluids Eng 118:4–17Google Scholar
  6. 6.
    Blackadar AK (1997) Turbulence and diffusion in the atmosphere. Springer, BerlinGoogle Scholar
  7. 7.
    Warhaft Z (2000) Passive scalar in turbulent flows. Annu Rev Fluid Mech 32:203–240CrossRefGoogle Scholar
  8. 8.
    Sawford B (2001) Turbulent relative dispersion. Annu Rev Fluid Mech 33:289–317CrossRefGoogle Scholar
  9. 9.
    Britter RE, Hanna SR (2003) Flow and dispersion in urban areas. Annu Rev Fluid Mech 35: 469–496CrossRefGoogle Scholar
  10. 10.
    Wang LP, Maxey MR (1993) Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J Fluid Mech 256:27–68CrossRefGoogle Scholar
  11. 11.
    Korolev AV, Mazin IP (1993) Zones of increased and decreased concentration in stratiform clouds. J Appl Meteorol 32:760–773CrossRefGoogle Scholar
  12. 12.
    Eaton JK, Fessler JR (1994) Preferential concentration of particles by turbulence. Int J Multiphase Flow 20:169–209CrossRefGoogle Scholar
  13. 13.
    Fessler JR, Kulick JD, Eaton JK (1994) Preferential concentration of heavy particles in a turbulent channel flow. Phys Fluids 6:3742–3749CrossRefGoogle Scholar
  14. 14.
    Maxey MR, Chang EJ, Wang L-P (1996) Interaction of particles and microbubbles with turbulence. Exp Thermal Fluid Sci 12:417–425CrossRefGoogle Scholar
  15. 15.
    Sundaram S, Collins LR (1997) Collision statistics in a isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J Fluid Mech 335:75–109CrossRefGoogle Scholar
  16. 16.
    Kostinski AB, Shaw RA (2001) Scale-dependent droplet clustering in turbulent clouds. J Fluid Mech 434:389–398CrossRefGoogle Scholar
  17. 17.
    Aliseda A, Cartellier A, Hainaux F, Lasheras JC (2002) Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J Fluid Mech 468:77–105CrossRefGoogle Scholar
  18. 18.
    Shaw RA (2003) Particle-turbulence interactions in atmospheric clouds. Ann Rev Fluid Mech 35:183–227CrossRefGoogle Scholar
  19. 19.
    Collins LR, Keswani A (2004) Reynolds number scaling of particle clustering in turbulent aerosols. New J Phys 6:119 (1–17)Google Scholar
  20. 20.
    Chun J, Koch DL, Rani SL, Ahluwalia A, Collins LR (2005) Clustering of aerosol particles in isotropic turbulence. J Fluid Mech 536:219–251CrossRefGoogle Scholar
  21. 21.
    Ayyalasomayajula S, Gylfason A, Collins LR, Bodenschatz E, Warhaft Z (2006) Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys Rev Lett 97:144507 (1–4)Google Scholar
  22. 22.
    Pinsky M, Khain AP (1997) Formation of inhomogeneity in drop concentration induced by drop inertia and their contribution to the drop spectrum broadening. Quart J Roy Meteor Soc 123:165–186CrossRefGoogle Scholar
  23. 23.
    Vaillancourt PA, Yau MK (2000) Review of particle-turbulence interactions and consequences for Cloud Physics. Bull Am Met Soc 81:285–298CrossRefGoogle Scholar
  24. 24.
    Pinsky M, Khain AP, Shapiro M (2000) Stochastic effects on cloud droplet hydrodynamic interaction in a turbulent flow. Atmos Res 53:131–169CrossRefGoogle Scholar
  25. 25.
    Reade W, Collins LR (2000) Effect of preferential concentration on turbulent collision rates. Phys Fluids 12:2530–2540CrossRefGoogle Scholar
  26. 26.
    Hogan RC, Cuzzi JN (2001) Stokes and Reynolds number dependence of preferential particle concentration in simulated three-dimensional turbulence. Phys Fluids A13:2938–2945CrossRefGoogle Scholar
  27. 27.
    Bec J (2003) Fractal clustering of inertial particles in random flows. Phys Fluids 15:L81–L84CrossRefGoogle Scholar
  28. 28.
    Boffetta G, De Lillo F, Gamba A (2004) Large scale inhomogeneity of inertial particles in turbulent flows. Phys Fluids 16:L20–L23CrossRefGoogle Scholar
  29. 29.
    Elperin T, Kleeorin N, Rogachevskii I (1996) Turbulent thermal diffusion of small inertial particles. Phys Rev Lett 76:224–227CrossRefGoogle Scholar
  30. 30.
    Elperin T, Kleeorin N, Rogachevskii I (1996) Self-excitation of fluctuations of inertial particles concentration in turbulent fluid flow. Phys Rev Lett 77:5373–5376CrossRefGoogle Scholar
  31. 31.
    Elperin T, Kleeorin N, Rogachevskii I (1998) Dynamics of particles advected by fast rotating turbulent fluid flow: fluctuations and large-scale structures. Phys Rev Lett 81:2898–2901CrossRefGoogle Scholar
  32. 32.
    Elperin T, Kleeorin N, Rogachevskii I, Sokoloff D (2000) Turbulent transport of atmospheric aerosols and formation of large-scale structures. Phys Chem Earth A25:797–803CrossRefGoogle Scholar
  33. 33.
    Elperin T, Kleeorin N, Rogachevskii I, Sokoloff D (2001) Strange behavior of a passive scalar in a linear velocity field. Phys Rev E 63:046305 (1–7)Google Scholar
  34. 34.
    Kraichnan RH (1968) Small-scale structure of a scalar field convected by turbulence. Phys Fluids 11:945–953CrossRefGoogle Scholar
  35. 35.
    Elperin T, Kleeorin N, L’vov V, Rogachevskii I, Sokoloff D (2002) The clustering instability of inertial particles spatial distribution in turbulent flows. Phys Rev E 66:036302 (1–16)Google Scholar
  36. 36.
    Klyatskin VI (1994) Statistical description of the diffusion of tracers in a random velocity field. Sov Phys Usp 37:501–514Google Scholar
  37. 37.
    Elperin T, Kleeorin N, Rogachevskii I (1995) Dynamics of passive scalar in compressible turbulent flow: large-scale patterns and small-scale fluctuations. Phys Rev E 52:2617–2634CrossRefGoogle Scholar
  38. 38.
    Elperin T, Kleeorin N, Rogachevskii I (2000) Mechanisms of formation of aerosol and gaseous inhomogeneities in the turbulent atmosphere. Atmosph Res 53:117–129CrossRefGoogle Scholar
  39. 39.
    Buchholz J, Eidelman A, Elperin T, Grünefeld G, Kleeorin N, Krein A, Rogachevskii I (2004) Experimental study of turbulent thermal diffusion in oscillating grids turbulence. Exp Fluids 36:879–887CrossRefGoogle Scholar
  40. 40.
    Eidelman A, Elperin T, Kleeorin N, Krein A, Rogachevskii I, Buchholz J, Grünefeld G (2004) Turbulent thermal diffusion of aerosols in geophysics and in laboratory experiments. Nonlinear Processes Geophys 11:343–350Google Scholar
  41. 41.
    Eidelman A, Elperin T, Kleeorin N, Markovich A, Rogachevskii I (2006) Experimental detection of turbulent thermal diffusion of aerosols in non-isothermal flows. Nonlinear Processes Geophys 13:109–117Google Scholar
  42. 42.
    Eidelman A, Elperin T, Kleeorin N, Rogachevskii I, Sapir-Katiraie I (2006) Turbulent thermal diffusion in a multi-fan turbulence generator with the imposed mean temperature gradient. Exp Fluids 40:744–752CrossRefGoogle Scholar
  43. 43.
    Maxey MR, Corrsin S (1986) Gravitational settling of aerosol particles in randomly oriented cellular flow field. J Atmos Sci 43:1112–1134CrossRefGoogle Scholar
  44. 44.
    Maxey MR (1987) The gravitational settling of aerosol particles in homogeneous turbulence and random flow field. J Fluid Mech 174:441–465CrossRefGoogle Scholar
  45. 45.
    Balkovsky E, Falkovich G, Fouxon A (2001) Intermittent distribution of inertial particles in turbulent flows. Phys Rev Lett 86:2790–2793CrossRefGoogle Scholar
  46. 46.
    Landau LD, Lifshits EM (1987) Fluid mechanics. Pergamon, OxfordGoogle Scholar
  47. 47.
    Frisch U (1995) Turbulence: the Legasy of A. N. Kolmogorov. Cambridge University Press, CambridgeGoogle Scholar
  48. 48.
    L’vov VS, Procaccia I (1995) Exact resummation in the theory of hydrodynamic turbulence. 0. Line-resummed diagrammatic perturbation approach. In: Lecture Notes of the Les Houches summer school, “fluctuating geometries in statistical mechanics and field theory”, David F, Ginsparg P (eds) North-Holland, Amsterdam, pp 1027–1075Google Scholar
  49. 49.
    L’vov VS, Procaccia I (1995) Hydrodynamic turbulence. I. The ball of locality and normal scaling. Phys Rev E 52:3840–3857CrossRefGoogle Scholar
  50. 50.
    Zeldovich Ya.B, Molchanov SA, Ruzmaikin AA, Sokoloff DD (1988) Intermittency, diffusion and generation in a nonstationary random medium. Sov Sci Rev C Math Phys 7:1–110Google Scholar
  51. 51.
    Shandarin SF, Zeldovich Ya.B (1989) The large-scale structure of the Universe-turbulence, intermittency, structures in a self-gravitating medium. Rev Mod Phys 61:185–220CrossRefGoogle Scholar
  52. 52.
    Klyatskin VI, Saichev AI (1997) Statistical theory of the diffusion of a passive tracer in a random velocity field. Sov Phys JETP 84:716–724CrossRefGoogle Scholar
  53. 53.
    Seinfeld JH (1986) Atmospheric chemistry and physics of air pollution. John Wiley, New YorkGoogle Scholar
  54. 54.
    Flagan R, Seinfeld JH (1988) Fundamentals of air pollution engineering. Prentice Hall, Englewood CliffsGoogle Scholar
  55. 55.
    Pruppacher HR, Klett JD (1997) Microphysics of clouds and precipitation. Kluwer Academic Publishers, DordrechtGoogle Scholar
  56. 56.
    Hodgson LS, Brandenburg A (1998) Turbulence effects in planetesimal formation. Astron Astrophys 330:1169–1174Google Scholar
  57. 57.
    Bracco A, Chavanis PH, Provenzale A, Spiegel EA (1999) Particle aggregation in keplerian flows. Phys Fluids 11:2280–2293CrossRefGoogle Scholar
  58. 58.
    Crowe CT, Sommerfeld M, Tsuji Y (1998) Multiphase flows with particles and droplets. CRC Press, New YorkGoogle Scholar
  59. 59.
    Heywood JB (1988) Internal combustion engine fundamentals. MacGraw-Hill, Boston, New YorkGoogle Scholar
  60. 60.
    Borman GL, Ragland KW (1999) Combustion engineering. MacGraw-Hill, Boston, New-YorkGoogle Scholar
  61. 61.
    Duncan KP, Mehlig B, Östlund S, Wilkinson M (2005) Clustering in mixing flows. Phys Rev Lett 95:240602CrossRefGoogle Scholar
  62. 62.
    Mehlig B, Wilkinson M, Duncan KP, Weber T, Ljunggren M (2005) On the aggregation of inertial particles in random flows. Phys Rev E 72:051104CrossRefGoogle Scholar
  63. 63.
    Wilkinson M, Mehlig B (2005) Caustics in turbulent aerosols. Europhys Lett 71:186–192CrossRefGoogle Scholar
  64. 64.
    L’vov VS, Procaccia I (1995) Exact resummations in the theory of hydrodynamic turbulence. II. A ladder to anomalous scaling. Phys Rev E 52:3858–3875CrossRefGoogle Scholar
  65. 65.
    Elperin T, Kleeorin N, Rogachevskii I, Sokoloff D (2000) Passive scalar transport in a random flow with a finite renewal time: mean-field equations. Phys Rev E 61:2617–2625CrossRefGoogle Scholar
  66. 66.
    Elperin T, Kleeorin N, Rogachevskii I, Sokoloff D (2001) Mean-field theory for a passive scalar advected by a turbulent velocity field with a random renewal time. Phys Rev E 64:026304 (1–9)Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Tov Elperin
    • 1
    Email author
  • Nathan Kleeorin
    • 1
  • Michael A. Liberman
    • 2
  • Victor S. L’vov
    • 3
  • Igor Rogachevskii
    • 1
  1. 1.The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of PhysicsUppsala UniversityUppsalaSweden
  3. 3.Department of Chemical PhysicsThe Weizmann Institute of ScienceRehovotIsrael

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