A scalar patch forms spiral structure when it wraps around an isolated vortex. It is shown that this wind-up process leads to accelerated diffusion during a time range TS<t<TD. The lower limit TS is the time needed to create a well-defined spiral, and the upper limit TD is the diffusive time scale of the scalar field θ in the vortex. Whereas the scaling TD∼Pe1/3 is independent of the particular spiral topology, the accelerated decay of the scalar variance θ2[bar](t) for earlier times is directly linked to the space-filling property of the spiral and is found to scale as θ2[bar](0)−θ2[bar](t)∼ (Pe1/3t) 3(1−D′K). D′K is the Kolmogorov capacity of the spiral; it is defined in the range 1/2<D′K<1 and it is the most suitable measure of the spiral's space-filling property.