Geometry of particle paths in turbulent flows

We use the intrinsic geometrical characteristics of space curves, i.e. curvature and torsion, to describe the paths of particles passively advected in a turbulent flow. We find that curvature increases with the Reynolds number and that the maxima in vorticity and curvature times local velocity are linearly correlated. Fluctuations around the maximal values in runs at a fixed Reynolds number are only weakly correlated, and the distributions are fairly wide, so that it is not possible to conclude that a tightly wound spiral has to correspond to a region of high vorticity.