  Formation of stars is now believed to be tightly linked to the dynamical
evolution of interstellar filaments in which they form. In this paper we
analyze the density structure and kinematics of a small network of infrared
dark filaments, SDC13, observed in both dust continuum and molecular line
emission with the IRAM 30m telescope. These observations reveal the presence of
18 compact sources amongst which the two most massive, MM1 and MM2, are located
at the intersection point of the parsec-long filaments. The dense gas velocity
and velocity dispersion observed along these filaments show smooth, strongly
correlated, gradients. We discuss the origin of the SDC13 velocity field in the
context of filament longitudinal collapse. We show that the collapse timescale
of the SDC13 filaments (from 1 Myr to 4 Myr depending on the model parameters)
is consistent with the presence of Class I sources in them, and argue that, on
top of bringing more material to the centre of the system, collapse could
generate additional kinematic support against local fragmentation, helping the
formation of starless super-Jeans cores.
