We investigate theoretically and experimentally the stability of three interlaced helical vortices with respect to displacement disturbances whose wavelengths are large compared to the size of the vortex cores. A space-time analogy is used to present a model for the spatial evolution of semi-infinite helical vortices subjected to time-periodic disturbances. This model is used to investigate the spatially evolving wake of a three-bladed turbine, which is subject to the global or local pairing instability that represents different wake control strategies. Perturbations modify the minimal distance between neighboring pairs, but also their relative orientation, i.e., locally parallel, antiparallel, or perpendicular. This is relevant for vortex merging, but also for the development of elliptical and Crow instabilities.