We investigate two-dimensional vortex merging of three vortices, initially aligned and evenly spaced, with the two outer vortices having the same strength and the middle one having any strength. Based on the vorticity transport equation (VTE) a vortex is identified as an extremum of the vorticity. The vorticity is also investigated through the low-dimensional core-growth model, providing analytical insight into the vorticity patterns and transitions, including explicit formulas of trajectories of the critical points of vorticity. Four distinct vorticity patterns and four types of trajectories of the vorticity are found. For a corotating centre vortex there are two types of trajectories of the vorticity, one where the centre vortex dominates the two outer vortices, and one where the centre vortex is suppressed by the two outer vortices. The two types of trajectories are separated in parameter space by the strength ratio of the inner to outer vortex being 4 (-3/2). In the case of a counter-rotating vortex centre, the centre vortex is suppressed in the flow transitions for centre vortex strengths less than the sum of the two outer vortices. For a range of vortex strengths of the middle vortex, the three vortex configuration first rotates in one direction and then shifts direction of rotation. In the case of a centre vortex strength exceeding the sum of the two outer vortices, the two outer vortices are pushed away. The core-growth model quantitatively reproduces the VTE flow for low Reynolds number (Re) and topologically provides accurate descriptions up to Re = 1290 where filamentation vortices are created.
Andersen et al. (Mon,) studied this question.