  A new mixing layer can be generated if the rotation of either of the two
cylinders in a Taylor--Couette apparatus varies discontinuously along the
symmetry axis. The mixing zone between the two resulting co-current streams
gives rise to radial vorticity in addition to the primary axial vorticity. An
analytic solution for the azimuthal velocity has been derived from which we
show that the width of the mixing zone varies only with radial position.
