  Magnetic fields are an important component of the interstellar medium (ISM)
and exhibit strongly varying field strengths and a non-trivial correlation with
the gas density. Its dynamical impact varies between individual regions of the
ISM and correlates with the orientation of the field with respect to the gas
structures. Using high-resolution magneto-hydrodynamical simulations of the ISM
we explore the connection between the orientation of the field and the
dynamical state of the gas. We find that the onset of gravitational instability
in molecular gas above a density of $\rho\sim10^{-21}\,\mathrm{g\,cm^{-3}}$
$(n\sim400\,\mathrm{cm^{-3}})$ coincides with an alignment of the magnetic
field lines and the gas flow. At this transition the gradient of the density
changes from mainly perpendicular to preferentially parallel to the field
lines. A connection between the three-dimensional alignment and projected
two-dimensional observables is non-trivial, because of a large dispersion of
the magnetic field orientation along the line of sight. The turbulent
correlation lengths can be small compared to the typical integration lengths.
As a consequence the small scale signal of the orientation can sensitively
depend on the line of sight or the dynamical state of the cloud, can fluctuate
stochastically or be completely averaged out. With higher spatial resolution
more small scale structures are resolved, which aggravates the link between
magneto-hydrodynamical quantities and projected observables.
