  We investigate the internal kinematics of the young star-forming region NGC
346 in the Small Magellanic Cloud. We used two epochs of deep F555W and F814W
Hubble Space Telescope ACS observations with an 11-year baseline to determine
proper motions, and study the kinematics of different populations, as
identified by their color-magnitude diagram and spatial distribution
characteristics. The proper motion field of the young stars shows a complex
structure with spatially coherent patterns. NGC 346 upper-main sequence and
pre-main sequence stars follow very similar motion patterns, with the outer
parts of the cluster being characterized both by outflows and inflows. The
proper motion field in the inner ~10 pc shows a combination of rotation and
inflow, indicative of inspiraling motion. The rotation velocity in this regions
peaks at ~3 km/s, whereas the inflow velocity peaks at ~1 km/s. Sub-clusters
and massive young stellar objects in NGC 346 are found at the interface of
significant changes in the coherence of the proper motion field. This suggests
that turbulence is the main star formation driver in this region. The similar
kinematics observed in the metal-poor NGC 346 and the Milky Way star-forming
regions suggest that the differences in the cooling conditions due to the
different amounts of metallicity and dust density between the SMC and our
Galaxy are too small to alter significantly the process of star clusters
assembly and growth. The main characteristics of our findings are consistent
with various proposed star cluster formation models.
