Collision and reconnection of viscous elliptic vortex rings

It is well known that head-on collision of two identical circular vortex rings at moderate Reynolds numbers generates secondary vortex ringlets that propagate radially away from the center of the primary rings. In this paper, we show through numerical simulations that deforming vortex ring shape from a circle to an ellipse can lead to drastic changes in flow topology during the collision. The computations are performed for a range of flow parameters, including the aspect ratio of elliptic rings, the core size ratio (η), and the azimuthal angle between their major axes (θ). Results show that if two elliptic rings are identical and in the absence of azimuthal perturbation, the collision leads to the generation of two subelliptic vortex rings that propagate away from each other along a line approximately perpendicular to the original direction of approach of the primary rings. If, however, azimuthal perturbation is present, besides the two subelliptic rings, secondary vortex ringlets are generated on the remaining perimeter of the primary rings. On the other hand, if two primary elliptic rings are of unequal core sizes or if their major axes are not aligned to each other, the orientation and direction of travel of the two subelliptic rings generated deviate significantly from those involving two identical primary rings. If azimuthal perturbation is also present in these scenarios, more fine scale structures are generated and superimposed on the two subelliptic rings as well as the formation of secondary vortex ringlets. These findings may help us to explain some of the experimental observations reported in the literature and provide useful insights into the mixing processes of two directly opposed impinging elliptic jets.It is well known that head-on collision of two identical circular vortex rings at moderate Reynolds numbers generates secondary vortex ringlets that propagate radially away from the center of the primary rings. In this paper, we show through numerical simulations that deforming vortex ring shape from a circle to an ellipse can lead to drastic changes in flow topology during the collision. The computations are performed for a range of flow parameters, including the aspect ratio of elliptic rings, the core size ratio (η), and the azimuthal angle between their major axes (θ). Results show that if two elliptic rings are identical and in the absence of azimuthal perturbation, the collision leads to the generation of two subelliptic vortex rings that propagate away from each other along a line approximately perpendicular to the original direction of approach of the primary rings. If, however, azimuthal perturbation is present, besides the two subelliptic rings, secondary vortex ringlets are generated on the rem...