Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows*

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales. Here, we compare curvature and torsion probability density functions (PDFs) for Lagrangian trajectories obtained from experimental data using the Shake-the-Box algorithm for turbulent von Kármán flow, Rayleigh Bénard convection and a zero-pressure-gradient (ZPG) boundary layer over a flat plate. The results for the von Kármán flow and Rayleigh-Bénard convection compare and well  with those obtained previously from numerical data for homogeneous and isotropic turbulence. Results for the logarithmic layer within the boundary layer differ. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry of tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories.