An interactive geometrical organization of a vortex between vortical flow structure and bundle of vorticity lines

The present study analyses geometrical characteristics of vortical flow structure and bundle of vorticity lines in the core region of a vortex and their relationships. A Galilei invariant coordinate system, vortex space, in a vortex center clarifies the vortical flow structure and associated vortex stretching, and local axis geometry theory specifies geometrical characteristics of the bundle with respect to the passage through the swirl plane in the vortical region, applying the geometrical quantities swirlity, sourcity, and vortical flow symmetry. It indicates that the vortex stretching swirls a bundle of the vorticity lines, and that its feature depends on the geometrical dynamics of the velocity structure along a vortical region. On the other hand, the velocity structure is influenced by the geometry of a bundle of the vorticity lines, and swirling or rotating feature of the bundle generates the axial flow of the vortex. An analysis of them in a homogeneous isotropic turbulence with the Direct Numerical Simulation shows these interactive characteristics. It indicates that a vortex may have a mutual geometrical organization system of them.