  Recent observations of global velocity gradients across and along molecular
filaments have been interpreted as signs of gas accreting onto and along these
filaments, potentially feeding star-forming cores and proto-clusters. The
behavior of velocity gradients in filaments, however, has not been studied in
detail, particularly on small scales (< 0.1 pc). In this paper, we present
MUFASA, an efficient, robust, and automatic method to fit ammonia lines with
multiple velocity components, generalizable to other molecular species. We also
present CRISPy, a Python package to identify filament spines in 3D images
(e.g., position-position-velocity cubes), along with a complementary technique
to sort fitted velocity components into velocity-coherent filaments. In NGC
1333, we find a wealth of velocity gradient structures on a beam-resolved scale
of ~0.05 pc. Interestingly, these local velocity gradients are not randomly
oriented with respect to filament spines and their perpendicular, i.e., radial,
component decreases in magnitude towards the spine for many filaments. Together
with remarkably constant velocity gradients on larger scales along many
filaments, these results suggest a scenario in which gas falling onto filaments
is progressively damped and redirected to flow along these filaments.
