  Recent observations of neutral Galactic interstellar medium showed that
filamentary structures of HI clouds are aligned with the interstellar magnetic
field. Many interesting applications are proposed based on the alignment such
as measurement of magnetic field strength through the Chandrasekhar-Fermi
method and removal of polarized foreground dust emissions for the detection of
inflationary polarized emission in the cosmic microwave background radiation.
However, the physical origin of the alignment remains to be explained. To
understand the alignment mechanism, we examine formation of HI clouds triggered
by shock compression of diffuse warm neutral medium using three-dimensional
magnetohydrodynamic simulations with the effects of optically thin cooling and
heating. We show that the shock-compressed diffuse interstellar medium of
density n~1 cm^-3 evolves into HI clouds with typical density n~50 cm^-3 via
thermal instability driven by cooling, which is consistent with previous
studies. We apply a machine vision transformation developed by Clark et
al.(2014) to the resulting column density structures obtained by the
simulations in order to measure angle correlation between filamentary
structures of HI clouds and magnetic field. We find that the orientation of HI
filaments depends on the environmental turbulent velocity field, particularly
on the strength of shear strain in the direction of the magnetic field, which
is controlled by the angle between the shock propagation direction and upstream
magnetic field. When the strain along the magnetic field is weak, filamentary
components of HI clouds basically lie perpendicular to the magnetic field.
However, the filaments have come to align with the magnetic field, if we
enhance the turbulent strain along the magnetic field or if we set turbulence
in the preshock medium.
