The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is
considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations
on a time scale of order P1/3 times the turn-over time, where P is a Péclet number.
The mechanism relies on differential rotation, that is, a non-zero gradient of angular
velocity. However if the flow is smooth, the gradient of angular velocity necessarily
vanishes at the centre of the streamlines, and the time scale becomes greater. The
behaviour at the centre is analysed and it is found that scalar there is only destroyed
on a time scale of order P1/2. Related results are obtained for magnetic field and
for weak vorticity, a scalar coupled to the stream function of the flow. Some exact
solutions are presented.