Two point-like vortices with the same vorticity in 2D perfect fluid can rotate forever. Why do finite-sized vortices merge as soon as they touch? Why in general 2D fluid vortices of the same sign want to merge? Is there any analogy between vortex merging and droplet merging, i.e. is there something similar to surface tension for vortices?
From the abstract of "The physical mechanism of symmetric vortex merger: A new viewpoint":
Their 'results suggest that a complete merging process is as follows: the vortices deform first due to the mutually induced straining; the deformation results in elliptical vortices and an angle between the major axis of each elliptical vortex and the line joining the two vortices, which in turn cause an attraction of fluid particles from one vortex to the other; sheetlike vortex structures are thus formed; and finally the velocity field induced by these sheetlike structures readily pushes two vortex cores together.'
It also states that 'when the flow is viscous, the separation between vortices reduces and the mutual attraction increases with time by diffusion. As the mutual attraction dominates over the self-induced rotation, sheetlike structures are formed gradually and merger eventually occurs. The onset time of merger is thus found to depend not only on the initial separation but also on the Reynolds number. The former determines when the mutual attraction will become dominant and the latter controls the speed at which sheetlike structures grow.'