Liutex-based identification of multiple rebound events in co-rotating Lamb–Oseen vortex merging

The merging of co-rotating vortices is a canonical problem in vortex dynamics. Vortex centers are commonly identified by vorticity extrema, but late-stage shear-layer deformation can complicate their use as markers of compact rotational cores. This study uses Liutex to track vortex centers in co-rotating Lamb–Oseen pairs simulated with a lattice Boltzmann method. The vorticity-based results reproduce the established merging stages. For the representative equal-circulation case at R e = 2250 , vortex separation is also evaluated using Q maxima, Lagrangian tracer-cloud centroids, and finite-area vorticity centroids. All five measures identify the first rebound at closely matched times, and the nearly identical Lagrangian and vorticity-extremum amplitudes show that the first rebound contains a material-motion component. Liutex yields a larger first-rebound amplitude and more clearly resolves smaller late-stage vortex-center relocations, which remain sensitive to the center definition. The accompanying vorticity, Liutex, and shear fields show that these differences coincide with a redistribution of shear around the vortex cores. For unequal-circulation pairs, the weaker core eventually ceases to possess a distinct Liutex maximum during entrainment, while the local Liutex strength at the stronger-vortex center provides an auxiliary measure of its late-stage rotational-core evolution. A weakly perturbed three-dimensional vortex-tube case shows the same qualitative distinction, with | R | concentrated around compact rotational structures while broader | ω | regions coincide with elevated | S | . These results distinguish the well-supported first rebound from smaller, diagnostic-dependent late-stage events and clarify the role of shear-reduced vortex-center tracking.