Vortical flow characteristics derived from local flow geometry and relationships to bundle of vorticity lines in organization of vortical structure

The present study investigates geometrical features of vortical flow structure and relationships to geometry of bundle of vorticity lines passing through a vortical region. A Galilei invariant coordinate system, i.e., vortex space associated with the local flow geometry, is defined in a vortex center, where the swirl plane and directions of both elliptic vortical flow and inflow/outflow are specified. The local flow geometry at the center derives primary geometrical features of radial and azimuthal flows as specific quadratic forms around the center in the swirl plane of a finite scale vortex, and the vortex space derives universal expression of the velocity gradient tensor where the gradient of an axial flow in the plane is given. If a bundle of vorticity lines swirls in the plane, this geometry operates the second derivative of the axial flow, and induces it even if the pressure gradient gives force in the opposite direction. While the vortical flow structure generates the geometrical features of the bundle of vorticity lines in a vortical region, the bundle contributes to the generation of the axial flow. A vortical analysis in homogeneous isotropic turbulence with Direct Numerical Simulation shows these complementary characteristics.