The present investigation introduces a parameter to represent symmetry of a vortex. An important feature of a vortex to be identified in many fluid engineering fields is its stability derived from the flow kinematics, which is associated with the symmetry of its vortical flow. Although many vortex definitions and identification methods have been proposed in terms of various physical aspects of a vortex, such symmetry property or its identification is lacked. We focus on the flow geometry specified by the velocity gradient tensor, and show that the feature of its complex eigenvectors derives the symmetry of the vortical flow in the swirl plane. This property is invariant, and extracts the high symmetry vortex or vortical region irrespective of the intensity of the vortex. It does not require additional calculation except the complex eigenvectors, but it brings useful information of the flow state and skewness of vortices.

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