Inhomogeneous distribution of water droplets in cloud turbulence

Itzhak Fouxon, Yongnam Park, Roei Harduf, and Changhoon Lee
Phys. Rev. E 92, 033001 – Published 1 September 2015

Abstract

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.

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  • Received 23 September 2014
  • Revised 22 July 2015

DOI:https://doi.org/10.1103/PhysRevE.92.033001

©2015 American Physical Society

Authors & Affiliations

Itzhak Fouxon1,*, Yongnam Park2, Roei Harduf3, and Changhoon Lee1,2,†

  • 1Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea
  • 2Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
  • 3Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

  • *itzhak8@gmail.com
  • clee@yonsei.ac.kr

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Issue

Vol. 92, Iss. 3 — September 2015

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