Geometric nature of particle trajectories in isotropic turbulence

Characteristics of curvature and torsion of particle trajectories are investigated by using direct numerical simulations. Curvature, torsion and their ratio are expected to have crucial roles in identification of the vortical structures. Curvature and torsion are highly intermittent and their PDFs show a rigorous slope in log-log scale which indicates selfsimilar power-law behavior. It is well known that extremely high curvature comes from nearly zero-velocity event, but for the case of torsion it is not clealy explained. We found that the magnitude of torsion is determined mainly by the magnitude of |a|/|an||u|, but detailed physical interpretation of |a|/|an||u| is required. Enstrophy-conditional PDF and various Stokes number cases for heavy particles are also investigated, but they give almost the same shape of PDF, and that self-similar characteristics of curvature and torsion are not related with turbulent structures.