  We consider as base flow the stationary vortex filament solution obtained by
Castillo- Castellanos et al. (2021) in the far-wake of a rotor with
tip-splitting blades. The cases of a single blade and of two blades with a hub
vortex are studied. In these solutions, each blade generates two closely spaced
co-rotating tip vortices that form a braided helical pattern in the far-wake.
The long-wave stability of these solutions is analysed using the same vortex
filament framework. Both the linear spectrum and the linear impulse response
are considered. We demonstrate the existence of different types of instability
modes. A first type corresponds to the local pairing of consecutive turns of
the helical pattern, which is well described by the instability of an uniform
helical vortex with a core size given by the mean separation distance of the
vortices in the pair. A second type corresponds to the pairing of consecutive
turns of vortex pair and is observed only for densely braided patterns, which
is well described by the instability of two interlaced helical vortices by
straightening out the baseline helix. A third type of unstable modes modifies
the separation distance between the vortices in each pair and amplifies
specific (linear) wavelengths. These unstable modes also spread spatially with
a weaker rate.
