  Jet fragmentation is investigated through a Direct Numerical Simulation
campaign using Basilisk (Popinet & collaborators 2013). The simulations span
over one order of magnitude of gaseous Weber numbers (13 to 165), i.e. over the
second wind-induced and atomization regimes, and the jets develop over
distances up to 28 nozzle diameters. The study focuses on the size and velocity
distributions of droplets, as well as their joint distribution. Two models
derived from different theoretical backgrounds, the statistical description of
the turbulence intermittency (Novikov & Dommermuth 1997) and the empirical
description of the ligament-mediated fragmentation (Villermaux et al. 2004),
are compared for describing the droplet size distribution close to the nozzle.
The characteristics of the size-velocity joint distribution are explained using
the vortex ring theory (Saffman 1992) which highlights two sources of
fragmentation. Finally, the joint histogram of the particulate Reynolds and
Ohnesorge numbers is analysed and a normalisation is suggested. It reveals that
the delimitations of the droplet phase space, once properly normalised, are
self-similar and independent of the gaseous Weber number, both numerically and
experimentally.
