The passing feature of the bundles of the vortical axes, and topological relationships between the vortex and the vortical axes in an isotropic homogeneous turbulence*

The present study analyses the characteristics of the vorticity lines, the eigen-vortical-axis lines, and the pressure minimum lines in the vortical regions, and analyses the topological relationships in the three lines. This analysis applies the physical quantity called swirlity φ that evaluates the unidirectionality and intensity of azimuthal components of the subjected vector field. It also applies the theory of local axis geometry to analyse the topological characteristics of the above three lines in the vortical region. The results show that the vorticity lines and the pressure minimum lines have a swirling feature, while the eigen-vortical-axis lines do not tend to swirl in the vortical region. And, it shows that the directions of the rotation of the vorticity lines and the pressure minimum lines may be changed with the intensity of swirling along a vortical region. In addition, the angles between the two tangential vectors in the three lines show that the directions of the vorticity lines and the pressure minimum lines have a high correlation. Therefore, these two lines have a similar feature of the passage in the vortical region.