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 as temporal derivatives up to order 3 are involved. One might expect that the statistics of these observables depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh–Bénard convection and a zero-pressure-gradient turbulent boundary layer over a flat plate. The results for the von Kármán flow compare well with experimental results for the curvature PDF and results obtained by numerical simulations of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh–Bénard convection agree with those measured for von Kármán flow, while results for the logarithmic layer within the boundary layer differ slightly. We provide a potential explanation for the latter. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or 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.