title: Inhomogeneous distribution of water droplets in cloud turbulence.
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.
authors.affiliation: Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea.
authors.forename: Itzhak
authors.initials: I
authors.lastname: Fouxon
authors.affiliation: Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea.
authors.forename: Yongnam
authors.initials: Y
authors.lastname: Park
authors.affiliation: Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
authors.forename: Roei
authors.initials: R
authors.lastname: Harduf
authors.affiliation: Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea.|Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea.
authors.forename: Changhoon
authors.initials: C
authors.lastname: Lee