The existing studies on vortex rings have concentrated on non-zero circulation. However, the cases of zero circulation may also be significantly noteworthy on both theoretical and practical grounds. As the first attempt on this subject, in this paper a family of viscous laminar vortex rings with zero circulation and a moderate ratio of core radius to ring radius is studied using numerical simulations of the incompressible Navier–Stokes equations. This unusual zero circulation is achieved by assigning a special layered vorticity distribution with alternate signs to the vortex core. At the initial moment, the ring is axisymmetric, swirl-free and of a circular cross-section. It is found that the axial symmetry and the non-swirl nature of the vortex ring are preserved during the evolution, and the vortex ring endures a transition from the initial layered structure to a shell structure, then degenerates to an ordinary vortex ring with non-zero circulation at last. Significant vorticity cancellation is observed due to the interactions among the layered structures. A new Reynolds number, based on the absolute value of vorticity, is applied to the zero-circulation vortex rings in the present work. For such vortex rings, cases of both zero and non-zero vortical impulse can happen, unlike the ordinary ones with only non-zero vortical impulse. Additionally, it is found that the vortical impulse can be irrelevant to the ring diameter. The study may shed light on modelling certain real flows characterised by distinct vortex structures or configurations.
Zhang et al. (Thu,) studied this question.
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