We numerically investigate the driving of MHD turbulence by gravitational
contraction using simulations of an initially spherical, magnetically
supercritical cloud core with initially transonic and trans-Alfv\'enic
turbulence. We perform a Helmholtz decomposition of the velocity field, and
investigate the evolution of its solenoidal and compressible parts, as well as
of the velocity component along the gravitational acceleration vector, a proxy
for the infall component of the velocity field. We find that: 1) In spite of
being supercritical, the core first contracts to a sheet perpendicular to the
mean field, and the sheet itself collapses. 2) The solenoidal component of the
turbulence remains at roughly its initial level throughout the simulation,
while the compressible component increases continuously. This implies that
turbulence does {\it not} dissipate towards the center of the core. 3) The
distribution of simulation cells in the B-ρ plane occupies a wide
triangular region at low densities, bounded below by the expected trend for
fast MHD waves (B∝ρ, applicable for high local Alfv\'enic Mach
number \Ma) and above by the trend expected for slow waves (B∼
constant, applicable for low local \Ma). At high densities, the distribution
follows a single trend B \propto \rho^{\gamef}, with 1/2 < \gamef < 2/3, as
expected for gravitational compression. 4) The measured mass-to-magnetic flux
ratio λ increases with radius r, due to the different scalings of the
mass and magnetic flux with r. At a fixed radius, λ increases with
time due to the accretion of material along field lines. 5) The solenoidal
energy fraction is much smaller than the total turbulent component, indicating
that the collapse drives the turbulence mainly compressibly, even in directions
orthogonal to that of the collapse.Comment: Resubmitted to MNRAS after first set of reviewer's recommendations.
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