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Acceleration of rain initiation by cloud turbulence


Vapour condensation in cloud cores produces small droplets that are close to one another in size. Droplets are believed to grow to raindrop size by coalescence due to collision1,2. Air turbulence is thought to be the main cause for collisions of similar-sized droplets exceeding radii of a few micrometres, and therefore rain prediction requires a quantitative description of droplet collision in turbulence1,2,3,4,5. Turbulent vortices act as small centrifuges that spin heavy droplets out, creating concentration inhomogeneities6,7,8,9,10,11,12,13,14 and jets of droplets, both of which increase the mean collision rate. Here we derive a formula for the collision rate of small heavy particles in a turbulent flow, using a recently developed formalism for tracing random trajectories15,16. We describe an enhancement of inertial effects by turbulence intermittency and an interplay between turbulence and gravity that determines the collision rate. We present a new mechanism, the ‘sling effect’, for collisions due to jets of droplets that become detached from the air flow. We conclude that air turbulence can substantially accelerate the appearance of large droplets that trigger rain.

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Figure 1: Normalized effective collection kernel for equal-size droplets at Re 106 according to equations (2), (3), (4) and (6).
Figure 2: Distribution over sizes after 10 min.


  1. Pruppacher, H. & Klett, J. Microphysics of Clouds and Precipitation (Kluwer, Dordrecht, 1998)

    Google Scholar 

  2. Seinfeld, J. & Pandis, S. Atmospheric Chemistry and Physics (Wiley, New York, 1998)

    Google Scholar 

  3. Pinsky, M., Khain, A. & Shapiro, M. Stochastic effects of cloud droplet hydrodynamic interaction in a turbulent flow. Atmos. Res. 53, 131–169 (2000)

    Article  Google Scholar 

  4. Jonas, P. Turbulence and cloud microphysics. Atmos. Res. 40, 283–306 (1996)

    Article  CAS  Google Scholar 

  5. Vaillancourt, P. A. & Yau, M. K. Review of particle-turbulence interactions and consequences for cloud physics. Bull. Am. Met. Soc. 81, 285–298 (2000)

    Article  Google Scholar 

  6. Maxey, M. R. The gravitational settling of aerosol particles in homogeneous turbulence and random flow field. J. Fluid Mech. 174, 441–465 (1987)

    Article  ADS  Google Scholar 

  7. Squires, K. & Eaton, J. Measurements of particle dispersion from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 226, 1–35 (1991)

    Article  ADS  CAS  Google Scholar 

  8. Pinsky, M. & Khain, A. Turbulence effects on droplet growth and size distribution in clouds—a review. J. Aerosol Sci. 28, 1177–1214 (1997)

    Article  ADS  CAS  Google Scholar 

  9. Sundaram, S. & Collins, L. Collision statistics in an isotropic particle-laden turbulent suspension. J. Fluid Mech. 335, 75–109 (1997)

    Article  ADS  CAS  Google Scholar 

  10. Zhou, Y., Wexler, A. & Wang, L.-P. Modelling turbulent collision of bidisperse inertial particles. J. Fluid Mech. 433, 77–104 (2001)

    Article  ADS  CAS  Google Scholar 

  11. Reade, W. & Collins, L. Effect of preferential concentration on turbulent collision rates. Phys. Fluids 12, 2530–2540 (2000)

    Article  ADS  CAS  Google Scholar 

  12. Wang, L. P. & Maxey, M. Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68 (1993)

    Article  ADS  CAS  Google Scholar 

  13. Balkovsky, E., Falkovich, G. & Fouxon, A. Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett. 86, 2790–2793 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Brumfiel, G. How raindrops form. Phys. Rev. Focus 7, story 14 (22 March 2001),

  15. Shraiman, B. & Siggia, E. Scalar turbulence. Nature 405, 639–646 (2000)

    Article  ADS  CAS  Google Scholar 

  16. Falkovich, G., Gawedzki, K. & Vergassola, M. Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  17. Pinsky, M., Khain, A. & Shapiro, M. Collision efficiency of drops in a wide range of Reynolds numbers. J. Atmos. Sci. 58, 742–766 (2001)

    Article  ADS  Google Scholar 

  18. Johnson, D. B. The role of giant and ultragiant aerosol particles in warm rain initiation. J. Atmos. Sci. 39, 448–460 (1982)

    Article  ADS  Google Scholar 

  19. Levin, Z., Wurzler, S. & Reisin, T. Modification of mineral dust particles by cloud processing and subsequent effects on drop size distribution. J. Geophys. Res. 105, 4501–4512 (2000)

    Article  ADS  Google Scholar 

  20. Saffman, P. & Turner, J. On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30 (1956)

    Article  ADS  Google Scholar 

  21. Raju, N. & Meiburg, N. The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. Phys. Fluids 7, 1241–1264 (1995)

    Article  ADS  CAS  Google Scholar 

  22. Maxey, M. R. & Riley, J. J. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889 (1983)

    Article  ADS  Google Scholar 

  23. Vekshtein, G. Physics of Continuous Media: A Collection of Problems with Solutions 93–94 (Adam Hilger, Bristol, 1992)

    Google Scholar 

  24. Grits, B., Pinsky, M. & Khain, A. Formation of small-scale droplet concentration inhomogeneity in a turbulent flow as seen from experiments with an isotropic turbulence model. Proc. 13th Int. Conf. on Clouds and Precipitation Vol. 1, 138–141 (Am. Met. Soc., Reno, 2000).

  25. Kostinski, A. & Shaw, R. Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech. 434, 389–398 (2001)

    Article  ADS  CAS  Google Scholar 

  26. Brenguier, J.-L. & Chaumat, L. Droplet spectra broadening in cumulus clouds. J. Atmos. Sci. 58, 628–641 (1999)

    Article  ADS  Google Scholar 

  27. Belin, F., Maurer, J., Tabeling, P. & Willaime, H. Velocity gradient distribution in fully developed turbulence: an experimental study. Phys. Fluids 9, 3843–3850 (1997)

    Article  ADS  CAS  Google Scholar 

  28. Davila, J. & Hunt, J. C. R. Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117–145 (2001)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Crowe, C. T., Chung, J. N. & Troutt, T. R. Particulate Two Phase Flow Ch. 18 (ed. Roce, M. C.) 626 (Butterworth-Heinemann, Oxford, 1993)

    Google Scholar 

  30. Marble, F. E. Dynamics of dusty gases. Annu. Rev. Fluid Mech. 2, 397–461 (1970)

    Article  ADS  Google Scholar 

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We thank A. Khain, V. Lebedev and M. Pinsky for discussions, and the Minerva and Israel Science Foundations for support.

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Correspondence to G. Falkovich.

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Falkovich, G., Fouxon, A. & Stepanov, M. Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154 (2002).

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