Abstract
An invariant derived from complex eigenvectors of velocity gradient tensor is applied to analyze the local topology of vortices in vortex identification, as a parameter representing the symmetry of vortical flow.
The eigenvalues and eigenvectors of the velocity gradient tensor specify an intensity and direction of a vortex in the vortex identification. However, it is difficult to specify the symmetry of the vortical flow, which is associated with stability of a vortex. The ratio of norms of real and imaginary vectors of the complex eigenvectors is an invariant and used as a parameter to specify the symmetry of the vortical flow in the swirl plane, which enables to analyze and visualize the symmetry of vortices besides the vortex identification.
The relationships between the intensity and symmetry (the invariant) of vortices in isotropic decaying turbulence show that this symmetry property is high in the core region of a vortex, and that it is associated with the development and decay of a vortex.
