Vortex ring-vortex tube interactions

Numerical simulations of the interaction between the vortex ring and the vortex tube was performed, with the aim of control of tumbulent mixing layer. The vortex tube is the simple model of the rolling-up vortices in the mixing layer. The simulation was made by the three-dimensional vortex blob method. The ratio of circulation of vortex tube to vortex ring Γ_R/Γ_F was varied in the range of 0.5-2.0. If Γ_R/Γ_F = 0.5 the vortex was stretched and involved into the vortex tube. If Γ_R/Γ_F = 1.0 the cut and reconnection occurred between a part of the vortex ring and a part of the vortex tube. But if Γ_R/Γ_F exceeds about 1.5 the vortex ring was found to pass through the vortex tube. The initial position of the vortex ring has significant effects on the interaction. A portion in the vortex ring whose circulation is the same sign as the vortex tube, combined with the vortex tube to generate the large vortex. On the other hand, another portion in the vortex ring of the opposite sign generate a new vortex pair.