Hot wire measurement of cross-linking and unlinking in uniting two circular vortex rings

A laminar circular vortex ring with excellent reproducibility can be generated by pushing a mass of air through a circular orifice drilled on a buffer plate placed in front of a loudspeaker, which is driven by a stepwise voltage signal. In order to obtain complete information concerning the velocity fields during the 'uniting' of two circular vortex rings, phase-locked velocity measurement was carried out by using a single inclined hot wire point by point all over the flow field, and the vorticity fields were computed from the measured velocity fields. The vortex tubes representing the vortex rings were computed as well as the behavior of the fluid material initially held within the vortex ring, and the important differences among the vorticity, vortex tubes, and fluid materials being transported by following the velocity field were explained so as not to misread the real phenomenon and the substance of the physical mechanism. The through process can be divided into the terms of formation and approaching, first cross-linking and unlinking, second cross-linking and unlinking and decay. The first cross-linking and unlinking is 'positive' and finishes successfully by the continuous and increasing driving force on the adjoined original 'near' segments being pressed against each other, while the second cross-linking and unlinking is 'negative' and depends on the initial condition due to the monotonously decreasing driving force on the adjoined original 'far' segments in the united vortex ring. As the continuous induced velocities on the approaching and adjoining segments force the segments harder against each other, the flow region in their gap is narrowed, and immediately after, the gap cannot hold the whole flux; the flow overflows outward to create another velocity gradient that is observed as the sudden appearance of two new concentrated vorticity regions between the adjacent vortex tubes. Therefore, the vorticity in the adjoined original vortex tubes is transported, although no vorticity cancellation is recognized in the present measurement because the time scale of cancellation is much longer than that of the cross-linking and unlinking.