Geometrical properties of bundle of vortical axis lines in a vortical region and its relationships to vortical flow characteristics in turbulent vortices*

This study analyzes curvature properties of bundle of vortical axis lines and its relationships to topology of vortical flow in DNS (Direct Numerical Simulations). Vortical regions are identified using swirlity that specifies vortical/non-vortical feature and the intensity of azimuthal flow component in terms of local topology. Bundles of vortical axis lines apply to vorticity lines, pressure minimum lines, and eigen-vortical-axis lines. The topology of these bundles is also analyzed with local axis geometry theory using physical quantities of the local topology, and the geometrical properties are analyzed by assessing curvature.

The results of the analysis show that the curvature of all vortical axis lines identified using the Frenet-Serret formulas has little correlation with the topology of bundles of vortical axis lines in swirl plane and vortical flow. Vorticity line seems to have a correlation with the vortex stretching whereas pressure minimum line and eigen-vortical-axis line have less correlation with the stretching.