Circulation Measurements of Merging Vortex Rings

Abstract

Circulation measurements of merging vortex rings were performed in an unstratified fluid to determine the circulation loss during vortex reconnection. The rings were generated by pistons, aligned with a 15-degree difference between the two propagation directions. Circulation measurements were made in two measurement planes. A front view plane, in the plane of the generators and the centers of the two vortex rings, was used to measure the circulations of the vortex rings before reconnection. A side view plane, oriented symmetrically between the generators and orthogonal to the front view plane, was used to measure the circulations of the vortex rings emerging from the reconnection. The circulations of both laminar and turbulent vortices were measured. The measurements show that over 90% of the circulation is conserved during the reconnection of both laminar and turbulent vortex rings. Thus, almost no circulation was lost (beyond natural single-ring decay) between the vortices that disappeared in the front view and reappeared in the side view for either laminar or turbulent vortex rings. These results suggest that, while the vortex cells may be laminar or turbulent, their cores are laminar and reconnection is essentially a laminar process. These results also suggest that when aircraft line vortices evolve into vortex rings, when the flow is unstratified, the circulations of these rings will be nearly the same as the circulations of the line vortices before reconnection.