  This study is motivated by recent observations on the ubiquitous interstellar
density filaments and guided by the modern theory of magnetohydrodynamic (MHD)
turbulence. The interstellar turbulence shapes the observed density structure.
The perpendicular turbulent mixing, as the fundamental dynamics of MHD
turbulence, naturally entails parallel filaments presented in both the diffuse
medium and molecular clouds (MCs). The minimum width is determined by the
perpendicular neutral-ion decoupling scale in partially ionized media.
Differently, dense perpendicular filaments arise in highly supersonic
turbulence in MCs as a result of shock compression. Their width specifically
depends on the turbulence properties. We demonstrate that different alignments
of filaments with respect to the magnetic field originate from the varying
turbulence properties in the multi-phase interstellar medium.
