A number of systematic procedures for the identification of vortices/coherent structures have been developed as a way to address their possible kinematical and dynamical roles in structural formulations of turbulence. It has been broadly acknowledged, however, 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" (λci-criterion), which is critically revisited in this work. We classify the instances where the accuracy of the λci-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, ω) -the "vorticity curvature criterion" (λω-criterion) -which improves over the results obtained with the λci-criterion in controlled Monte-Carlo tests. A particularly problematic issue, given its importance in wall-bounded flows, is the eventual inadequacy of the λci-criterion for many-vortex configurations in the presence of strong background shear. We show that the λω-criterion is able to cope with these cases as well, 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 threedimensional extension of the λω-criterion. In contrast to the λci-criterion, the λω-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.

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analyzed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation, and velocity gradient invariants Q and R and their joint spatial distibutions, using data from a direct numerical simulation of isotropic turbulence at Re λ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus a geometric characterization in terms of these sets' correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behavior. Nevertheless the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on the multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow. We show that sets defined by joint conditions on strain and enstrophy, and on Q and R, also display power law scaling of correlation functions, providing further characterization of the complex spatial structure of these intersection sets.arXiv:1708.05409v1 [physics.flu-dyn]

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