  (Abbreviated) We investigate the interplay between magnetic (B) field,
gravity, and turbulence in the fragmentation process of cores within the
filamentary infrared dark cloud G34.43+00.24. We observe the magnetic field (B)
morphology across G34.43 and compare with the kinematics obtained from N2H+
across the filament. We derive local velocity gradients from N2H+, tracing
motion in the plane of sky, and compare with the observed local B field
orientations in the plane of sky. Besides a large-scale east-west velocity
gradient, we find a close alignment between local B field orientations and
local velocity gradients toward the MM1/MM2 ridge. This local correlation in
alignment suggests that gas motions are influenced by the magnetic field
morphology or vice versa. Additionally, this alignment seems to be getting even
closer with increasing integrated emission in N2H+, possibly indicating that a
growing gravitational pull is more and more aligning B field and gas motion. We
analyze and quantify B field, gravity, turbulence, and their relative
importance toward the MM1, MM2 and MM3 regions with various techniques over two
scales, a larger clump area at 2 pc scale and the smaller core area at 0.6 pc
scale. While gravitational energy, B field, and turbulent pressure all grow
systematically from large to small scale, the ratios among the three
constituents develop clearly differently over scale. We propose that this
varying relative importance between B field, gravity, and turbulence over scale
drives and explains the different fragmentation types seen at sub-pc scale (no
fragmentation in MM1; aligned fragmentation in MM2; clustered fragmentation in
MM3). We discuss uncertainties, subtleties, and the robustness of our
conclusion, and we stress the need of a multi-scale joint analysis to
understand the dynamics in these systems.
