  Interstellar gas clouds are often both highly magnetized and supersonically
turbulent, with velocity dispersions set by a competition between driving and
dissipation. This balance has been studied extensively in the context of gases
with constant mean density. However, many astrophysical systems are contracting
under the influence of external pressure or gravity, and the balance between
driving and dissipation in a contracting, magnetized medium has yet to be
studied. In this paper we present three-dimensional (3D) magnetohydrodynamic
(MHD) simulations of compression in a turbulent, magnetized medium that
resembles the physical conditions inside molecular clouds. We find that in some
circumstances the combination of compression and magnetic fields leads to a
rate of turbulent dissipation far less than that observed in non-magnetized
gas, or in non-compressing magnetized gas. As a result, a compressing,
magnetized gas reaches an equilibrium velocity dispersion much greater than
would be expected for either the hydrodynamic or the non-compressing case. We
use the simulation results to construct an analytic model that gives an
effective equation of state for a coarse-grained parcel of the gas, in the form
of an ideal equation of state with a polytropic index that depends on the
dissipation and energy transfer rates between the magnetic and turbulent
components. We argue that the reduced dissipation rate and larger equilibrium
velocity dispersion produced by compressing, magnetized turbulence has
important implications for the driving and maintenance of turbulence in
molecular clouds, and for the rates of chemical and radiative processes that
are sensitive to shocks and dissipation.
