Accumulation rates of spiral-like structures in fluid flows

Spiral-like structures in the passive scalar fields of typical fluid flows are examined with special reference to their rate of accumulation. The study was motivated in the particular context of the Kolmogorov capacity of such structures and their role in potentially dominating the measured dimension of iso-scalar contours in fully turbulent flows, but it may have broader implications. A specific conclusion is that the structures occurring in these flows are better modeled by a logarithmic spiral rather than a power-law spiral, and therefore do not make significant contributions to the empirical estimates of dimensions by box-counting methods. Another conclusion is that, at least for the Reynolds numbers examined here, the spiral-like structures (such as they are) rarely possess more than four or five turns.