Comment on “Axial stretching and vortex definition” [Phys. Fluids 17, 038108 (2005)]

In a recent paper, Wu, Xiong, and Yang hereafter referred to as WXY use local flow kinematics to i explain the differences between the Q, , and 2 vortex identification criteria and ii propose a general requirement mandatory for any definition of a vortex. Using Burgers and Sullivan vortices as analytical test cases, WXY compare the different vortex criteria based on their proposed vortex definition. Our research group has been using local flow kinematics to understand the relationship between various local vortex identification schemes and our work is comprehensively reported in a recent paper hereafter referred to as CBA . Over the years this work at various stages of its development has been reported in a number of conferences and archival publications. Both CBA and WXY use two local kinematic parameters, ci and cr / ci, to explore the relationships between the Q, , and 2 criteria. These relationships are used to understand the differences between these criteria. In the interpretation of cr / ci, however, there is a fundamental difference between CBA and WXY: CBA use cr / ci as a local measure of the orbital compactness of the instantaneous streamlines projected on the vortex plane, whereas WXY interpret cr / ci to be a measure of the axial strain. WXY’s interpretation is valid only in an incompressible flow, where the real eigenvalue satisfies the relation r=−2 cr. This interpretation of cr / ci is tied to their requirements for a vortex definition, to which we now focus attention. WXY propose that any vortex definition should be independent of the axial strain. Using this definition, they analyze the Burgers and Sullivan vortices. They conclude that the Q and 2 criteria are deficient, since the vortex size extracted by them depends on the axial strain rate, . Based on the following scaling argument, we claim that this analysis and consequently the conclusion are flawed. For these test vortices, consider and / as velocity and length scales, respectively, to make the velocity field nondimensional. In a Burgers vortex, the velocity field becomes