Numerical simulation and flow-visualization experiment on deformation of pseudo-elliptic vortex rings

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Abstract
The deformation of a pseudo-elliptic vortex ring with circulation Γ was studied by a three-dimensional vortex blob method which included the viscous diffusion of vorticity. The circumference of this vortex ring consisted of two parallel line segments of the same length connected by two semicircles of the same radius R, the length of the major axis being denoted by L. The cross section of the vortex ring was represented by multiple vortex blobs with overlapping cores, while the circumference of the vortex ring was divided into a number of such sections. Numerical calculations were performed for the aspect ratios L/2R = 2.0–12.0, the initial core radius σcs= 0.20R, and Reynolds number Γ/v = 1500, v being the kinematic viscosity. The vortex rings yielded four fundamental patterns of deformation which included the axis switching and the split, depending on the aspect ratio. A flow-visualization experiment confirmed three of the four fundamental patterns, and was in sufficient agreement with the computation for the period of the axis switching and the time of the split.

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