The vortex wandering mechanism is a topic worthy of study in vortex dynamics for both internal and external flows. Through the linear stability analysis, the instability mode of the circumferential wave number m=1 of the vortex most easily excited by the long-wave disturbance was proved from two aspects: the highest energy transport efficiency and the lowest viscous dissipation rate. And the analytical formula for displacement wandering was derived. The Crow instability phenomenon of the vortex rings was captured through time-resolved Particle image velocimetry in the starting jet. When a pair of vortex rings pinches off, they wander up and down at the far wake and eventually fuze. Dynamic mode decomposition was carried out through the snapshot of the flow field, and the most unstable mode existing in the flow field was captured, with a frequency of 2.7 Hz. In a confined space, a theoretical model of vortex wandering under vortex-acoustic resonance was established. The source of the vortex disturbance that causes rotating instability in the compressor is vortex wandering, and the theoretical relationship between rotating instability and nonsynchronous vibration is established through the vorticity moment theorem, further deepening the research on the vortex dynamics of internal flow.
Gao et al. (2025) studied this question.