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We investigate the Kelvin-Helmholtz instability occuring at the interface ofa shear flow configuration in 2D compressible magnetohydrodynamics (MHD). Thelinear growth and the subsequent non-linear saturation of the instability arestudied numerically. We consider an initial magnetic field aligned with theshear flow, and analyze the differences between cases where the initial fieldis unidirectional everywhere (uniform case), and where the field changes signat the interface (reversed case). We recover and extend known results for purehydrodynamic and MHD cases with a discussion of the dependence of thenon-linear saturation on the wavenumber, the sound Mach number, and theAlfvenic Mach number for the MHD case.  A reversed field acts to destabilize the linear phase of the Kelvin-Helmholtzinstability compared to the pure hydrodynamic case, while a uniform fieldsuppresses its growth. In resistive MHD, reconnection events almost instantlyaccelerate the buildup of a global plasma circulation. They play an importantrole throughout the further non-linear evolution as well, since the initialcurrent sheet gets amplified by the vortex flow and can become unstable totearing instabilities forming magnetic islands. As a result, the saturationbehaviour and the overall evolution of the density and the magnetic field ismarkedly different for the uniform versus the reversed field case.Comment: 19 pages, 12 figures, accepted by Journal of Plasma Physics, uses  JPP.st

Growth and saturation of the Kelvin–Helmholtz instability with parallel and antiparallel magnetic fields