Interaction of unequal anti-parallel vortex tubes

A computational study is reported of the close interaction of nominally ant i-parallel vortex tubes with unequal strengths, Gamma (1) and -Gamma (2), w here Gamma (2)/Gamma (1) less than or equal to 1. The computations are perf ormed 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 m utual interaction. The numerical method is tested for the case of equal-str ength vortices, which exhibits the classic vortex reconnection phenomenon t ypified by bridging between the vortex cores and formation of thin vorticit y threads as the bridged sections advect away under their self-induced velo city. Computations for vortices of unequal strengths are reported for cases with small, moderate and large strength differences, for which Gamma (2)/G amma (1) = 0.82, 0.54 and 0.25 are chosen as representative values. The bri dges between the vortex structures form loops that twist owing to the unequ al vortex strengths. In the thread region, the vortex interaction is contro lled by competition between the effects of stretching of the weak vortex as it wraps around the stronger vortex and the core distortion induced on eac h vortex owing to the straining imposed by the opposing vortex. For cases w ith large vortex strength difference, the strong vortex remains nearly stra ight as the weak vortex wraps around it, inducing an interlaced pattern of positive and negative vorticity spirals within the core of the strong vorte x. Over long time, the bridge regions form loops that propagate away from t he thread region for cases with small strength difference and wrap around t he nearly columnar strong vortex for cases with large strength difference.