A Lagrangian approach to identifying vortex pinch-off

A criterion for identifying vortex ring pinch-off based on the Lagrangian coherent structures (LCSs) in the flow is proposed and demonstrated for a piston-cylinder arrangement with a piston stroke to diameter (L/D) ratio of approximate to 12. It is found that the appearance of a new disconnected LCS and the termination of the original LCS are indicative of the initiation of vortex pinch-off. The subsequent growth of new LCSs, which tend to roll into spirals, indicates the formation of new vortex cores in the trailing shear layer. Using this criterion, the formation number is found to be 4.1 +/- 0.1, which is consistent with the predicted formation number of approximate to 4 of Gharib [Gharib J. Fluid Mech. 360, 121 (1998)]. The results obtained using the proposed LCS criterion are compared with those obtained using the circulation criterion of Gharib and are found to be in excellent agreement. The LCS approach is also compared against other metrics, both Lagrangian and Eulerian, and is found to yield insight into the pinch-off process that these do not. Furthermore, the LCS analysis reveals a consistent pattern of coalescing or pairing of adjacent vortices in the trailing shear layer, a process which has been extensively documented in circular jets. Given that LCSs are objective and insensitive to local errors in the velocity field, the proposed criterion has the potential to be a robust tool for pinch-off identification. In particular, it may prove useful in the study of unsteady and low Reynolds number flows, where conventional methods based on vorticity prove difficult to use.