On the relationships between local vortex identification schemes

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Vortex identification: New requirements and limitations (2007, background): “This aspect has led Cucitore et al. (1999) to introduce the concept of non-locality for determining the vortices as structures.”
Unsteady force generation and vortex dynamics of pitching and plunging aerofoils (2012, positive): “A popular method of identifying the vortex core and its boundary is to perform point-wise analysis of the velocity gradient tensor [89].”
Definitions of vortex vector and vortex (2017, background): “…most recent λω-criterion (Elsas & Moriconi 2017) are representative among many of the popular Eulerian local vortex identification methods which are based on the local pointwise analysis of the velocity gradient tensor (Chakraborty et al. 2005) and they meet the requirement of Galilean invariance.”
The onset of dynamic stall revisited (2012, background): “As a direct consequence, unambiguous vortex detection remains elusive and various Eulerian and Lagrangian criteria have been introduced whose adequateness depends on the specific problem at hand (Cucitore et al 1999; Chakraborty et al 2005).”
Defining coherent vortices objectively from the vorticity (2015, background): “The decomposition in (10) is a right-type decomposition, i.”