%0 Journal Article
%T Universal statistics of density of inertial particles sedimenting in turbulence
%A Itzhak Fouxon
%A Yongnam Park
%A Roei Harduf
%A Changhoon Lee
%J Physics
%D 2014
%I arXiv
%X We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio $Fr$ 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 $D_{KY}$. When inertia is not small $D_{KY}$ 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.
%U http://arxiv.org/abs/1409.5856v4