Inhomogeneous distribution of water droplets in cloud turbulence

Itzhak Fouxon, Yongnam Park, Roei Harduf, Changhoon Lee

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


We consider sedimentation of small particles in the turbulent flow where fluid accelerations are much smaller than acceleration of gravity g. The particles are dragged by the flow by linear friction force. We demonstrate that the pair-correlation function of particles' concentration diverges with decreasing separation as a power law with negative exponent. This manifests fractal distribution of particles in space. We find that the exponent is proportional to ratio of integral of energy spectrum of turbulence times the wave number over g. The proportionality coefficient is a universal number independent of particle size. We derive the spectrum of Lyapunov exponents that describes the evolution of small patches of particles. It is demonstrated that particles separate dominantly in the horizontal plane. This provides a theory for the recently observed vertical columns formed by the particles. We confirm the predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include conditions that hold for water droplets in warm clouds thus providing a tool for the prediction of rain formation.

Original languageEnglish
Article number033001
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
Publication statusPublished - 2015 Sept 1

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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