  We investigate the Kelvin-Helmholtz instability occuring at the interface of
a shear flow configuration in 2D compressible magnetohydrodynamics (MHD). The
linear growth and the subsequent non-linear saturation of the instability are
studied numerically. We consider an initial magnetic field aligned with the
shear flow, and analyze the differences between cases where the initial field
is unidirectional everywhere (uniform case), and where the field changes sign
at the interface (reversed case). We recover and extend known results for pure
hydrodynamic and MHD cases with a discussion of the dependence of the
non-linear saturation on the wavenumber, the sound Mach number, and the
Alfvenic Mach number for the MHD case.
  A reversed field acts to destabilize the linear phase of the Kelvin-Helmholtz
instability compared to the pure hydrodynamic case, while a uniform field
suppresses its growth. In resistive MHD, reconnection events almost instantly
accelerate the buildup of a global plasma circulation. They play an important
role throughout the further non-linear evolution as well, since the initial
current sheet gets amplified by the vortex flow and can become unstable to
tearing instabilities forming magnetic islands. As a result, the saturation
behaviour and the overall evolution of the density and the magnetic field is
markedly different for the uniform versus the reversed field case.
