Pinch-off of axisymmetric vortex pairs in the limit of vanishing vortex line curvature

What is it about?

The manuscript considers a topic of generally broad interest, namely, a limiting process (referred to as “pinch off”) in the transient formation of vortex rings and vortex pairs. A number of papers have been published on this topic over the preceding 17 years with emphasis ranging from theoretical vortex dynamics, to fluid mixing, to aquatic propulsion. The specific focus of this manuscript is how nature of the pinch off process changes under the constraint of planar 2D flow, rather than the more typical case of axisymmetric flow. The topic of vortex dipole formation and pinch off in planar 2D flows has received some attention recently and continues to be an area of research, with a key element of the investigations being a fundamental difference compared to axisymmetric flows, namely, that no pinch off is observed in the planar 2D case.

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Why is it important?

The present manuscript, we believe, explains the reason for this difference by showing that adding even a slight amount of curvature to the vortex lines allows the pinch off process to proceed normally. That is, no pinch off is observed in the 2D case because it is, in some sense, over-constrained (or artificially constrained).