Mechanism of "Cut and Connection" Phenomenon of Two Vortex Rings.

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In order to investigate the mechanism of "cut and connection" phenomenon of two vortex rings, interaction of two vortex rings with equivalent circulation on the same plane in infinite region is simulated by a finite difference method solving three-dimensional Navier-Stokes equation. As the "cut and connection" occurs, the vorticity disappears in the vicinity region of two vortex rings, while the bridge is produced and then two vortex rings are connected in both sides of the region where the vorticity is canceled. Each term of the vorticity equation was examined for investigating dominant factor in cut and connection phenomenon. We found following two results; the cancellation of vorticity is due to the convection term of the vortex equation and this result is consistent with the fact that there is intensified flow in the near region of vortex rings. It is observed that the viscous term is dominant factor for the bridging and the vorticity diffusion induced connecting both the peak values or the bottom values on the distribution of the vorticity, which yields forming the bridges between two vortex rings.
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