Merging of two helical vortices

Vortex merging is a basic fluid phenomenon which has been much studied for two-dimensional flows. Here we extend such a study to a specific class of three-dimensional flows, namely to vortices possessing a helical symmetry. In addition to the standard Reynolds number, this introduces another dimensionless control number, the pitch, which quantifies the periodicity length along the helix axis. Helical vortices with large pitches merge very much as in a two-dimensional setting. However, their rotation speed is reduced and the merging period is delayed. These effects, caused by the presence of a self-induced velocity in curved three-dimensional vortices, are understood by computing the streamfunction in the frame of reference rotating with the two vortices, and by inspecting the locations of its hyperbolic points. At intermediate pitch values, only viscous diffusion acts, resulting in a slow viscous type of merging. Finally for small pitches, the system is unstable resulting, at the nonlinear stage, in a different type of merging which breaks the initial central symmetry.