  Floating offshore wind turbines (FOWTs) are subjected to platform motion
induced by wind and wave loads. The oscillatory movement trigger vortex
instabilities, modifying the wake structure, influencing the flow reaching
downstream wind turbines. In this work, the wake of a FOWT is analysed by means
of numerical simulations and comparison with linear stability theory. Two
simplified models based on the stability of vortices are developed for all
degrees of freedom of turbine motion. In our numerical simulations, the wind
turbine blades are modeled as actuator lines and a spectral-element method with
low dispersion and dissipation is employed to study the evolution of the
perturbations. The turbine motion excites vortex instability modes predicted by
the linear stability of helical vortices. The flow structures that are formed
in the non-linear regime are a consequence of the growth of these modes and
preserve some of the characteristics that can be explained and predicted by the
linear theory. The number of vortices that interact and the growth rate of
disturbances are well predicted by a simple stability model of a
two-dimensional row of vortices. For all types of motion, the highest growth
rate is observed when the frequency of motion is one and a half the frequency
of rotation of the turbine; that induces the out-of-phase vortex pairing
mechanism. For lower frequencies of motion, several vortices coalesce to form
large flow structures, which cause high amplitude of oscillations in the
streamwise velocities, that may increase fatigue or induce high amplitude
motion on downstream turbines.
