  Magnetic fields are a dynamically important agent for regulating structure
formation in the interstellar medium. The study of the relative orientation
between the local magnetic field and gas (column-) density gradient has become
a powerful tool to analyse the magnetic field's impact on the dense gas
formation in the Galaxy. In this study, we perform numerical simulations of a
non-gravitating, isothermal gas, where the turbulence is driven either
solenoidally or compressively. We find that only simulations with an initially
strong magnetic field (plasma-$\beta<1$) show a change in the preferential
orientation between the magnetic field and isodensity contours, from mostly
parallel at low densities to mostly perpendicular at higher densities. Hence,
compressive turbulence alone is not capable of inducing the transition observed
towards nearby molecular clouds. At the same high initial magnetisation, we
find that solenoidal modes produce a sharper transition in the relative
orientation with increasing density than compressive modes. We further study
the time evolution of the relative orientation and find that it remains
unchanged by the turbulent forcing after one dynamical timescale.
