  Exact solutions of a magnetized plasma in a vorticity containing shear flow
for constant temperature are presented. This is followed by the modification of
these solutions by thermomagnetic currents in the presence of temperature
gradients. It is shown that solutions which are unstable for a subsonic flow,
are stable if the flow is supersonic.
  The results are applied to the problem of vorticity shear flow stabilization
of a linear z-pinch discharge.
