Accelerated scaler dissipation in a vortex

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 T-S < t < T-D. The lower limit T-S is the time needed to create a well-defined spiral, and the upper limit T-D is the diffusive time scale of the scalar field theta in the vortex. Whereas the scaling T-D similar to Pe(1/3) is independent of the particular spiral topology, the accelerated decay of the scalar variance <(theta(2))over bar>(t) for earlier times is directly linked to the space-filling property of the spiral and is found to scale as <(theta(2))over bar>(0)-<(theta(2))over bar>(t) similar to (Pe(-1/3)t)(3(1-DK')). 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.