Vortex identification: New requirements and limitations

Firstly, a brief survey dealing with popular vortex-identification methods is presented. The most widely used local criteria (applied point by point) – sharing a basis in the velocity-gradient tensor ∇u – are treated more thoroughly to recall their underlying ideas and physical aspects. A large number of recent papers have pointed out various applicability limitations of these popular schemes and formulated (explicitly or implicitly) new general requirements, for example: validity for compressible flows and variable-density flows, determination of the local intensity of swirling motion, vortex-axis identification, non-local properties, ability to provide the same results in different rotating frames, etc. Other quite natural requirements are pointed out and added to those already mentioned. Secondly, the vortex-identification outcome of the proposed triple decomposition of the relative motion near a point is presented. The triple decomposition of motion – based on the extraction of a so-called “effective” pure shearing motion – has been motivated by the fact that vorticity cannot distinguish between pure shearing motions and the actual swirling motion of a vortex. This decomposition technique results in two additive vorticity parts (and, analogously, in two additive strain-rate parts) of distinct nature, namely the shear component and the residual one. The residual vorticity represents a direct measure of the actual swirling motion of a vortex. The new kinematic vortex-identification method is discussed on the background of previous methods and general vortex-identification requirements (illustrative examples are included).