  Protoplanetary disks are gaseous systems in Keplerian rotation around young
stars, known to be turbulent. They include a small fraction of dust from which
planets form. In the incremental scenario for planet growth, the formation of
kilometer-size objects (planetesimals) from pebbles is a major open question.
Clustering of particles is necessary for solids to undergo a local
gravitational collapse. To address this question, the dynamic of inertial
particles in turbulent flows with Keplerian rotation and shear is studied.
Two-dimensional direct numerical simulations are performed to explore
systematically two physical parameters: the rotation rate, which depends on the
distance to the star, and the particle response time, which relates to their
size. Shear is found to drastically affect the characteristics of the turbulent
flow destroying cyclones and favoring the survival of anticyclones. Faster
Keplerian rotation enhances clustering of particles. For intermediate sizes,
particles concentrate in anticyclones. These clusters form in a hierarchical
manner and merge together with time. For other parameter values, solids
concentrate on fractal sets that get more singular with rotation. The mass
distribution of particles is then found to be multifractal with small
dimensions at large orders, intriguing for triggering their gravitational
collapse. Such results are promising for a precise description and better
understanding of planetesimal formation.
