4D visualization study of a vortex ring life cycle using modal analyses

Abstract

In this study, the life cycle of a vortex ring is visualized and simultaneously investigated in a three-dimensional (3D) domain and time resolved for an observer in a reference frame moving with the ring. By traversing the system, the object of interest is captured within the measurement volume during the entire cycle. The 4D (time-resolved 3D) data gained from the experiment are postprocessed by using modal analyses such as proper orthogonal decomposition and dynamic mode decomposition (DMD). The latter is used to reconstruct the vortex dynamics by means of the Q values, based on the most dominant modes in the DMD. These modal analyses allow reconstructing the dominant dynamics of the behavior of the secondary structures and their interaction with the vortex core. The visualization for the vortex ring at Re Γ = 5500 shows the well-known azimuthal instability and its growth at n = 6 in our experiments. As the process of transition further develops, we found a zig-zag-like mesh of tilted secondary structure and finally, helical coil-type vortex ribbons wrapped around the core, which emerge in the late-stage process. It is hypothesized that the initial state of this process is the emergence of a pair of standing helical waves both counterbalancing each other at the beginning and forming the zig-zag pattern. Azimuthal core flow is only weak in this phase. Later in the transition, one of the helical waves starts to take over the other and finally dominates. This results in the helical coil-type vortex structure seen in the reconstructed results, which goes with the increase in axial flow along the core. The hypothesis of coexisting helical waves is drawn from similarities in the transition of attached vortex rings in axisymmetric wakes.