Disappearing vortex problem in vortex identification: Non-existence for selected criteria

Abstract

A discontinuous outcome of vortex-identification methods called the disappearing vortex problem (DVP) has been already found for the swirling strength criterion and the Rortex (later renamed as Liutex) method. Here, the opposite property reflecting the situation that the DVP cannot be found for any input data, that is, the non-existence of the DVP, is examined and proved valid for selected criteria based on the velocity-gradient tensor, including Q, lambda-2, and the triple decomposition method. For the Q-criterion and the triple decomposition method, it is done directly, whereas for lambda-2, it is shown using a proof by contradiction.

Velocity gradient analysis of a head-on vortex ring collision

“…The philosophical distinction between symmetry-based and geometry-based criteria also underlies the so-called ‘disappearing vortex problem’ in which, fixing the VGT configuration and strain rate, increasing only the vorticity magnitude can remove a geometry-based vortex from the flow (Chakraborty et al. 2005; Kolář & Šístek 2020, 2022). However, we here adopt the geometry-based viewpoint since, unlike vorticity, rigid rotation persistently underlies rotational local streamline topologies in all inertial frames.…”