We solve the problem of spatial distribution of inertial particles that sediment in turbulent flow with small ratio of acceleration of fluid particles to acceleration of gravity g. The particles are driven by linear drag and have arbitrary inertia. The pair-correlation function of concentration obeys a power-law in distance with negative exponent. Divergence at zero signifies singular distribution of particles in space. Independently of particle size the exponent is ratio of integral of energy spectrum of turbulence times the wavenumber to g times numerical factor. We find Lyapunov exponents and confirm predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include typical case of water droplets in clouds. This significant progress in the study of turbulent transport is possible because strong gravity makes the particle's velocity at a given point unique.PACS numbers: 47.10. Fg, 05.45.Df, 47.53.+n Inhomogeneity of distribution of water droplets in clouds, caused by air turbulence, is significant factor in the formation of rain [1][2][3]. Due to inhomogeneity droplets collide and coalesce more often speeding up the formation of larger drops. It rains when the drops get so large as to reach the ground without evaporating on the way.Turbulence-induced inhomogeneities of transported quantities could seem contradicting to the well-known mixing of turbulence producing uniform distribution [4]. Indeed mixing dominates on larger scales. On smaller scales turbulence produces highly irregular spatial structures. Similarly to ordinary centrifuges the rotating turbulent vortices push the inertial droplets out [5] causing very strong non-uniformities in droplets distribution to accumulate with time. Those occur at the typical scale of the vortices (the Kolmogorov scale) which is much smaller than the typical scale of the flow. Thus formation of inhomogeneities of particles by turbulence is small-scale phenomenon, often disregarded due to finite resolution of instruments. Since it is at those scales that droplets collide then the study of the inhomogeneities is necessary to predict rain formation.Much progress was obtained in the study of nonuniform distributions of inertial particles in the flow when gravity is negligible [1][2][3][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In the regime where the inertia is not too large, which is where turbulence is most relevant in the rain formation process [3], the paircorrelation function of concentration was demonstrated to obey a power-law with negative exponent signifying singular (fractal) structure formed by particles in space. Furthermore the leading order term for the exponent at small inertia was obtained for Navier-Stokes turbulence without model-dependent assumptions on the statistics * Electronic address: itzhak8@gmail.com † Electronic address: clee@yonsei.ac.kr of turbulence [1,6]. It depends on statistics of turbulence via the ratio of time integral of correlation function of laplacian of pressure divided by...

We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio F r of acceleration of fluid particles to acceleration of gravity g. The particles are driven by linear drag and have arbitrary inertia. We demonstrate that independently of the particles' size or density the particles distribute over fractal set with log-normal statistics determined completely by the Kaplan-Yorke dimension DKY . When inertia is not small DKY is proportional to the ratio of integral of spectrum of turbulence multiplied by wave-number and g. This ratio is independent of properties of particles so that the particles concentrate on fractal with universal, particles-independent statistics. We find Lyapunov exponents and confirm predictions numerically. The considered case includes typical situation of water droplets in clouds.