Interaction of unequal anti-parallel vortex tubes

A computational study is reported of the close interaction of nominally anti-parallel vortex tubes with unequal strengths, Gamma (1) and -Gamma (2), where Gamma (2)/Gamma (1) less than or equal to 1. The computations are performed using a spectral method, with periodic boundary conditions and vortex Reynolds number Re equivalent to Gamma (1)/v = 1500, and the vortices are perturbed by a wavelength for which the pair is unstable because of their mutual interaction. The numerical method is tested for the case of equal-strength vortices, which exhibits the classic vortex reconnection phenomenon typified by bridging between the vortex cores and formation of thin vorticity threads as the bridged sections advect away under their self-induced velocity. Computations for vortices of unequal strengths are reported for cases with small, moderate and large strength differences, for which Gamma (2)/Gamma (1) = 0.82, 0.54 and 0.25 are chosen as representative values. The bridges between the vortex structures form loops that twist owing to the unequal vortex strengths. In the thread region, the vortex interaction is controlled by competition between the effects of stretching of the weak vortex as it wraps around the stronger vortex and the core distortion induced on each vortex owing to the straining imposed by the opposing vortex. For cases with large vortex strength difference, the strong vortex remains nearly straight as the weak vortex wraps around it, inducing an interlaced pattern of positive and negative vorticity spirals within the core of the strong vortex. Over long time, the bridge regions form loops that propagate away from the thread region for cases with small strength difference and wrap around the nearly columnar strong vortex for cases with large strength difference.