On the relationships between different vortex identification methods based on local trace criterion

Vortical flow is generally considered to be a flow with a rotational trend, but vortex regions vary depending on the vortex identification methods by which they are extracted. In this paper, theoretical relationships between commonly used Q series vortex criteria, eigenvalue-based vortex criteria, and the Rortex method are analytically derived and built based on the local trace (LT) criterion ( L T cri). The projections of vortex regions extracted by different vortex criteria onto the LT-plane constructed by L T cri are presented to graphically discuss their physical meanings and interrelations. The L T cri-based method reflects the local swirling patterns of flow and provides new interpretations of various vortex criteria in terms of local flow patterns. The simple vortex models, including Rankin vortex and Burgers' vortex, forced isotropic turbulence flow, and a compressor corner separation flow case with a practical Mach number, are tested and analyzed. The potential of the L T cri-based method is shown both by analyzing vortex dynamic properties and by distinguishing the different swirling patterns of complex vortices in tangle. This contributes to the exploration of flow mechanisms and furthers investigations into vortex dynamics.