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 Karman flow, Rayleigh-Benard convection and a zero-pressure -gradient turbulent boundary layer over a flat plate. The results for the von Karman 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-Benard convection agree with those measured for von Karman 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.

Automated summary

Using curvature and torsion to describe Lagrangian trajectories provides insights into small and large time scales. Probability density functions (PDFs) of curvature and torsion were calculated for experimental Lagrangian trajectories in different flows, and were compared with experimental and numerical simulation results. The effect of anisotropy on geometry or tracer particle trajectories was quantified using the curvature vector, which was found to be related to velocity fluctuations.