Invariant characteristics of the eigen-vortical-axis line to pierce intense vortical region in multi-scale flows in an isotropic homogeneous turbulence

The present study investigates a feature of the eigen-vortical-axis line in terms of passing through intense vortical region in several decomposed flow scales in an isotropic homogeneous decaying turbulence in a low Reynolds number Re_λ ≈ 35. This axis line based on the invariant local flow topology has stronger characteristics to pierce intense vortical regions in terms of the swirlity or vorticity, and to be normal to the maximum plane of the swirlity than the vorticity line. It is noted that swirlity represents the unidirectionality and intensity of azimuthal flow in the geometrical mean. The maximum plane is specified by the Hessian of the swirlity. We decompose a turbulent flow using the Fourier band-pass filter, and investigate these characteristics in decomposed scale flows. The analyses in decomposed multi-scale flows show that the eigen-vortical-axis line has invariant characteristics to pierce intense vortical region and have stronger feature to be normal to the maximum plane of the swirlity than the vorticity line, irrespective of the flow scale.