Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Acceleration of rain initiation by cloud turbulence

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  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), http://focus.aps.org/v7/st14.html.

  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 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Falkovich.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Falkovich, G., Fouxon, A. & Stepanov, M. Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154 (2002). https://doi.org/10.1038/nature00983

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature00983

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing