  We present results of three-dimensional (3D) simulations of the
magnetohydrodynamic Kelvin-Helmholtz instability in a stratified shear layer.
The magnetic field is taken to be uniform and parallel to the shear flow. We
describe the evolution of the fluid flow and the magnetic field for a range of
initial conditions. In particular, we investigate how the mixing rate of the
fluid depends on the Richardson number and the magnetic field strength. It was
found that the magnetic field can enhance as well as suppress mixing. Moreover,
we have performed two-dimensional (2D) simulations and discuss some interesting
differences between the 2D and 3D results.
