Comparison of vortex identification criteria for planar velocity fields in wall turbulence

Abstract

This study derives and compares vortex identification methods for detecting vortices in planar velocity fields. Two-dimensional (2D) forms of the commonly used Δ, Q, λci, and λ2 criteria are derived in detail based on the 2D counterpart of the full velocity gradient tensor. These four criteria are compared mathematically and experimentally in the case of using zero thresholds. The results show that while all methods are capable of extracting strong vortices, their efficiencies in identifying weaker vortices are not necessarily the same. The Δ and λci criteria impose the least requirements on the identified structures and extract the most number of vortices, and the λ2 criterion is the most restrictive one and tends to discard the weakest vortices. However, non-zero thresholds are generally necessary for applying vortex identification criteria in real turbulent flows, and normalizing the vortex indicators with their root mean squares is needed to enable the selection of universal threshold for vortices residing at different wall-normal positions in wall turbulence. The introduction of threshold makes the four vortex identification criteria equally efficacious, and equivalent thresholds are proposed to facilitate quantitative comparison of results based on different criteria in wall turbulence.