Vortex identification from local properties of the vorticity field

Abstract

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” ( ci-criterion), which is critically revisited in this work. We classify the instances where the accuracy of the 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,!)—the “vorticity curvature criterion” ( !-criterion)—which improves over the results obtained with the ci-criterion in controlled Monte Carlo tests. A particularly problematic issue, given its importance in wall-bounded flows, is the eventual inadequacy of the ci-criterion for many-vortex configurations in the presence of strong background shear. We show that the !-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 of a turbulent channel flow, including a three-dimensional extension of the !-criterion. In contrast to the ci-criterion, the !-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.