  We have performed extensive two-dimensional magnetohydrodynamic simulations
to study the amplification of magnetic fields when a supernova blast wave
propagates into a turbulent interstellar plasma. The blast wave is driven by
injecting high pressure in the simulation domain. The interstellar magnetic
field can be amplified by two different processes, occurring in different
regions. One is facilitated by the fluid vorticity generated by the ``rippled"
shock front interacting with the background turbulence. The resulting turbulent
flow keeps amplifying the magnetic field, consistent with earlier work
\citep{Giacalone2007}. The other process is facilitated by the growth of the
Rayleigh-Taylor instability at the contact discontinuity between the ejecta and
the shocked medium. This can efficiently amplify the magnetic field and tends
to produce the highest magnetic field. We investigate the dependence of the
amplification on numerical parameters such as grid-cell size and on various
physical parameters. We show the magnetic field has a characteristic radial
profile that the downstream magnetic field gets progressively stronger away
from the shock. This is because the downstream magnetic field needs a finite
time to reach the efficient amplification, and will get further amplified in
the Rayleigh-Taylor region. In our simulation we do not observe a systematic
strong magnetic field within a small distance to the shock. This indicates that
if the magnetic-field amplification in supernova remnants indeed occurs near
the shock front, other processes such as three-dimensional instabilities,
plasma kinetics and/or cosmic ray effect may need to be considered to explain
the strong magnetic field in supernova remnants.
