  Recent Herschel observations of nearby clouds have shown that filamentary
structures are ubiquitous and that most prestellar cores form in filaments.
Probing the density ($n$) and velocity ($V$) structure of filaments is crucial
for the understanding of the star formation process. To characterize both the
$n$ and the $V$ field of a fragmenting filament, we mapped NGC2024. 13CO, C18O,
and H13CO+ trace the filament seen in the $N_{H_2}$ data. The radial profile
from the $N_{H_2}$ data shows $D_{HP}$~0.081 pc, which is similar to the
Herschel findings. The $D_{HP}$ from 13CO and C18O are broader, while the
$D_{HP}$ from H13CO+ is narrower, than $D_{HP}$ from Herschel. These results
suggest that 13CO and C18O trace only the outer part of the filament and H13CO+
only the inner part. The H13CO+ $V_{centroid}$ map reveals $V$ gradients along
both filament axis, as well as $V$ oscillations with a period $\lambda$~0.2 pc
along the major axis. Comparison between the $V$ and the $n$ distribution shows
a tentative $\lambda$/4 shift in H13CO+ or C18O. This $\lambda$/4 shift is not
simultaneously observed for all cores in any single tracer but is tentatively
seen in either H13CO+ or C18O. We produced a toy model taking into account a
transverse $V$ gradient, a longitudinal $V$ gradient, and a longitudinal
oscillation mode caused by fragmentation. Examination of synthetic data shows
that the oscillation component produces an oscillation pattern in the velocity
structure function (VSF) of the model. The H13CO+ VSF shows an oscillation
pattern, suggesting that our observations are partly tracing core-forming
motions and fragmentation. We also found that the mean $M_{core}$ corresponds
to the effective $M_{BE}$ in the filament. This is consistent with a scenario
in which higher-mass cores form in higher line-mass filaments.
