  Maps of polarized dust emission of molecular clouds reveal the morphology of
the magnetic field associated with star-forming regions. In particular,
polarization maps of hub-filament systems show the distortion of magnetic field
lines induced by gas flows onto and inside filaments. We aim to understand the
relation between the curvature of magnetic field lines associated with
filaments in hub-filament systems and the properties of the underlying gas
flows. We consider steady-state models of gas with finite electrical
resistivity flowing across a transverse magnetic field. We derive the relation
between the bending of the field lines and the flow parameters represented by
the Alfv\'en Mach number and the magnetic Reynolds number. We find that, on the
scale of the filaments, the relevant parameter for a gas of finite electrical
resistivity is the magnetic Reynolds number, and we derive the relation between
the deflection angle of the field from the initial direction (assumed
perpendicular to the filament) and the value of the electrical resistivity, due
to either Ohmic dissipation or ambipolar diffusion. Application of this model
to specific observations of polarized dust emission in filamentary clouds shows
that magnetic Reynolds numbers of a few tens are required to reproduce the
data. Despite significant uncertainties in the observations (the flow speed,
the geometry and orientation of the filament), and the idealization of the
model, the specific cases considered show that ambipolar diffusion can provide
the resistivity needed to maintain a steady state flow across magnetic fields
of significant strength over realistic time scales.
