We investigate the Kelvin–Helmholtz instability occurring
at the interface of a
shear-flow configuration in 2D compressible magnetohydrodynamics (MHD).
The
linear growth and the subsequent nonlinear saturation of the instability
are
studied numerically. We consider an initial magnetic field aligned with
the shear
flow, and analyse the differences between cases where the initial field
is unidirectional
everywhere (uniform case) and those 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 nonlinear saturation
on the wavenumber, the sound Mach number and the Alfvénic Mach number
for
the MHD case. A reversed field acts to destabilize the
linear phase of the Kelvin–Helmholtz instability compared with the
pure
hydrodynamic case, while a uniform
field suppresses its growth. In resistive MHD, reconnection events almost
instantly
accelerate the build up of a global plasma circulation. They play an important
role
throughout the further nonlinear evolution as well, since the initial current
sheet is
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 are markedly different for the uniform
versus
the reversed-field case.