Interaction of two axially-symmetric helical vortices

We studied the evolution of two equal, coaxial, symmetrically located helical vortices in an unbounded, inviscid, incompressible fluid. We computed the evolution with a triple-periodic vortex-in-cell method and found four main regimes of behavior: 1) Thin vortices translate and rotate uniformly while preserving their form, as predicted by Joukowsky (1912), and their velocities agree with those obtained by Velasco Fuentes (2018), 2) Thicker vortices behave as predicted by Joukowsky (1912) but they move with smaller velocities than the thin vortices studied by Velasco Fuentes (2018), 3) Fat, large-pitch vortices merge to form a single cylindrical column with mainly axial vorticity. This process is analogous to the merger of two Rankine vortices (which correspond to helical vortices of infinite pitch) but the vortices approach each other faster and merge even from relatively large distances (where Rankine vortices would not merge). 4) Small-pitch vortices merge to form a single cylindrical shell with mainly azimuthal vorticity. This occurs even for thin vortices if the pitch is sufficiently small.