Amplification of turbulence in contracting prestellar cores in
  primordial minihalos
  We investigate the amplification of turbulence through gravitational
contraction of the primordial gas in minihalos. We perform numerical
simulations to follow the cloud collapse, assuming polytropic equations of
state for different initial turbulent Mach numbers and resolutions. We find
that the turbulent velocity is amplified solely by gravitational contraction,
and eventually becomes comparable to the sound speed, even for small initial
turbulent Mach numbers (${\cal M}_0 \gtrsim 0.05$). We derive an analytic
formula for the amplification of turbulent velocity in a collapsing cloud, and
find that our numerical results are consistent with the formula. These results
suggest that the turbulence can play an important role in collapsing clouds for
general cases.
