  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.
