Skip to main content

Cloud Turbulence and Droplets

  • Conference paper
  • First Online:
Turbulent Cascades II

Part of the book series: ERCOFTAC Series ((ERCO,volume 26))

  • 590 Accesses

Abstract

Evolution of droplets and turbulence in a small box which is ascending inside the maritime cumulus cloud has seamlessly been simulated for about 10 min from the view point of the microscopic dynamics. It is found that the kinetic energy spectrum obeys the Kolmogorov spectrum \(k^{-5/3}\) at low to moderate wavenumbers, while the spectra of the temperature and the water vapor mixing ratio are modified, close to \(k^{-1/3}\) at low wavenumbers and roll off more slowly than the exponential in the diffusive range. This modification of the spectra arises from the condensation-evaporation and the liquid water mass loading to the flow. It is also found that the spectra related to the cloud droplets consist of two contributions, one is from the spatially correlated part and the other is from the uncorrelated part which originates from the discreteness of droplets. The former dominates the spectrum at low to moderate wavenumbers and the latter at high wavenumbers. We argue the effects of the two contributions on the turbulence spectra.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ayala, O., Rosa, B., Wang, L.-P., Grabowski, W.W.: Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 1. Results from direct numerical simulation. New J. Phys. 10, 075015 (2008)

    Article  Google Scholar 

  2. Devenish, B.J., Bartello, P., Brenguier, J.-L., Collins, L.R., Grabowski, W.W., IJzermans, R.H.A., Malinowski, S.P., Reeks, M.W., Vassilicos, J.C., Wang, L.-P., Warhaft. Z.: Droplet growth in warm turbulent clouds. Q. J. R. Meteorol. Soc. 138, 1401–1429 (2012)

    Article  Google Scholar 

  3. Falkovich, G., Fouxon, A., Stepanov, M.G.: Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154 (2004)

    Article  Google Scholar 

  4. Gotoh, T., Suehiro, T., Saito, I.: Continuous growth of cloud droplets in cumulus cloud. New J. Phys. 18, 043042 (2016)

    Article  Google Scholar 

  5. Grabowski, W.W., Wang, L.-P.: Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324 (2013)

    Article  MathSciNet  Google Scholar 

  6. Hall, W.D.: A detailed microphysical model within a two-dimensional dynamic framework: model description and preliminary results. J. Atmos. Sci 37, 2486–2507 (1980)

    Article  Google Scholar 

  7. Landau, L.D., Lifshitz, E.M.: Statistical Physics. Third edition, Part 1, volume 5. Pergamon, Oxford, 1980

    Google Scholar 

  8. Onishi, R., Matsuda, K., Takahashi, K.: Lagrangian tracking simulation of droplet growth in turbulence? Turbulence enhancement of autoconversion rate. J. Atmos. Sci. 72, 2591–2607 (2015)

    Article  Google Scholar 

  9. Rosa, B., Parishani, H., Ayala, O., Grabowski, W.W., Wang, L.-P.: Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations. New J. Phys. 15, 045032 (2013)

    Article  Google Scholar 

  10. Saito, I., Gotoh, T.: Turbulence and cloud droplets in cumulus clouds. New J. Phys. 20, 023001 (2018)

    Article  Google Scholar 

  11. Sardina, G., Picano, F., Brandt, L., Caballero, R.: Continuous growth of droplet size variance due to condensation in turbulent clouds. Phys. Rev. Lett. 115, 1–5 (2015)

    Article  Google Scholar 

  12. Shaw, R.A.: Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227 (2003)

    Article  Google Scholar 

  13. Sundaram, S., Collins, L.R.: Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109 (1997)

    Article  Google Scholar 

  14. Sundaram, S., Collins, L.R.: A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105–143 (1999)

    Article  Google Scholar 

  15. Takahashi, T.: Warm rain development in a three-dimensional cloud model. J. Atmos. Sci. 71, 1991–2013 (1981)

    Article  Google Scholar 

  16. Vaillancourt, P.A., Yau, M.K., Grabowski, W.W.: Microscopic approach to cloud droplet growth by condensation. Part 1: model description and results without turbulence. J. Atmos. Sci. 58, 1945–1964 (2001)

    Article  Google Scholar 

  17. Vaillancourt, P.A., Yau, M.K., Bartello, P., Grabowski, W.W.: Microscopic approach to cloud droplet growth by condensation. Part II: turbulence, clustering, and condensational growth. J. Atmos. Sci. 59, 3421–3435 (2002)

    Article  Google Scholar 

  18. Wang, P.K.: Physics and Dynamics of Clouds and Precipitation. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

Download references

Acknowledgements

This research used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science, through the High Performance Computing Infrastructure (HPCI) System Research Project (hp160085, hp170189). The computational supports provided by Japan High Performance Computing and Networking, Large-scale Data Analyzing and Information Systems (JHPCN) (jh160012, jh170013), by High Performance Computing (HPC 2016) at Nagoya University and by “Plasma Simulator” under the auspices of the NIFS Collaboration Research program (NIFS16KNSS076) are also gratefully acknowledged. Development of some numerical codes used in this work was supported in part by the “Code development support program” of Numerical Simulation Reactor research Project (NSRP), NIFS. I. S. and T. G. and T. W. are supported by Grants-in-Aid for Scientific Research Nos. 15H02218, 26420106, respectively, from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Toshiyuki Gotoh .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Saito, I., Gotoh, T., Watanabe, T. (2019). Cloud Turbulence and Droplets. In: Gorokhovski, M., Godeferd, F. (eds) Turbulent Cascades II. ERCOFTAC Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-12547-9_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-12547-9_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12546-2

  • Online ISBN: 978-3-030-12547-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics