  Turbulence in an incompressible fluid with and without a magnetic field as
well as moderately compressible MHD turbulence are compared. For the
magnetohydrodynamic (MHD) models the probability distribution functions of the
velocity components perpendicular to the external magnetic field are like the
incompressible hydrodynamic (HD) model while those parallel to the field have a
smaller range of velocities. The probability distribution functions of the
transverse velocity increments for the MHD models decline slower than the
incompressible HD model. The similarity of incompressible HD and both
incompressible and compressible MHD turbulence persists over high order
longitudinal structure function scaling exponents measured in the global
reference frame as well as for motions perpendicular to the local mean field.
In these two frames the longitudinal scaling exponents of both MHD models seem
to follow theoretical incompressible HD dissipation structure predictions while
the transverse scaling exponents of the incompressible MHD model seem to follow
the predictions for incompressible MHD. In the local magnetic system the
motions parallel to the local mean field for both MHD models are different from
incompressible HD motions. The fields of the MHD simulations are decomposed
into Alfvenic, fast, and slow modes and stuided separately. (abridged)
