Vortex Identification from Local Properties of the Vorticity Field

It has been broadly acknowledged that vortex detection algorithms, usually based on linear-algebraic properties of the velocity gradient tensor, can be plagued with severe shortcomings and may become, in practical terms, dependent on the choice of subjective threshold parameters in their implementations. In two-dimensions, a large class of standard vortex identification prescriptions turn out to be equivalent to the "swirling strength criterion" ($\lambda_{ci}$-criterion), which is critically revisited in this work. We classify the instances where the accuracy of the $\lambda_{ci}$-criterion is affected by nonlinear superposition effects and propose an alternative vortex detection scheme based on the local curvature properties of the vorticity graph $(x,y,\omega)$ -- the "vorticity curvature criterion" ($\lambda_\omega$-criterion) -- which improves over the results obtained with the $\lambda_{ci}$-criterion in controlled Monte-Carlo tests. We show that the $\lambda_\omega$-criterion is able to cope with strong shear effects, if a subtraction of the mean velocity field background is performed, in the spirit of the Reynolds decomposition procedure. A realistic comparative study for vortex identification is then carried out for a direct numerical simulation (DNS) of a turbulent channel flow, including a three-dimensional extension of the $\lambda_\omega$-criterion. In contrast to the $\lambda_{ci}$-criterion, the $\lambda_\omega$-criterion indicates in a consistent way the existence of small scale isotropic turbulent fluctuations in the logarithmic layer, in consonance with long-standing assumptions commonly taken in turbulent boundary layer phenomenology.