The analysis of the topological characteristics of bundle of axes lines

This study focuses on the bundle of axes lines in an isotropic homogeneous turbulence, and analyses the topological characteristics of vorticity lines and eiven-vortical-axis lines passing the vortex region. The characteristics of bundles of axes lines are analysed using the theory of local axis geometry. This theory analyses quantitatively the characteristics of the bundle of axes lines with respect to the passage of vortical region by focusing on the gradient tensor of the subjected vector field with respect to swirl plane and evaluating the physical quantities derived from the tensor such as swirlity and sourcity in the swirl plane. The results of analysis using this theory show that vorticity lines have a swirling feature, whereas the eigen-vortical axis lines pass the core region without swirling. It is also shown that the difference of these axes lines derived from vortex stretching and topological feature of the vortex itself.