On the effectiveness and limitations of local criteria for the identification of a vortex

TLDR: In this paper, three local criteria for the identification of vortices are analyzed and discussed; they are based on the analysis of invariants of the velocity gradient tensor ▿u or invariant of the tensor S 2 + Ω 2, where S and Ω are the symmetric and antisymmetric parts of ▾u.

Abstract: Three proposed local criteria for the identification of vortices are analyzed and discussed; they are based on the analysis of invariants of the velocity gradient tensor ▿u or invariants of the tensor S 2 +Ω 2 , where S and Ω are the symmetric and antisymmetric parts of ▿u. Moreover, a tentative non-local procedure is proposed, which takes advantage of the observation that vortices tend to be made up of the same fluid particles; this leads to the definition of a Galilean invariant quantity, which can be computed and used to identify vortical structures. Three analytical flow fields are used for a comparative evaluation of both local and non-local criteria, which allows a deeper understanding of the physical meaning of the considered techniques.