Accelerated diffusion in the centre of a vortex

The spiral wind-up and diffusive decay of a passive scalar in circular stre amlines is considered. An accelerated diffusion mechanism operates to destr oy scalar fluctuations on a time scale of order P-1/3 times the turn-over t ime, where P is a Peclet number. The mechanism relies on differential rotat ion, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the cen tre of the streamlines, and the time scale becomes greater. The behaviour a t the centre is analysed and it is found that scalar there is only destroye d on a time scale of order P-1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of t he flow. Some exact solutions are presented.