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.

Floating offshore wind turbines (FOWTs) are the next frontier in offshore wind energy, allowing exploration of deep-water regions previously unavailable to fixed-foundation turbines. Since offshore turbines operate in lower turbulence levels, the intrinsic hydrodynamic unstable modes of the tip vortices can have even more relevance than in onshore turbines. For floating turbines, platform motion induced by wind and wave loads can trigger vortex instabilities, modifying the wake structure, possibly influencing the flow reaching downstream wind turbines. In the present paper, we study those effects by the means of numerical simulations and their comparison with analytical studies. In our simulations, the wind turbine blades are modeled as actuator lines in the incompressible Navier–Stokes equations. Heave motion with different amplitudes and frequencies are studied. The effect of increasing amplitude is to advance the onset of vortex interaction. For the lower frequency of heave motion, several vortices coalesce to form a large flow structure. High amplitude of oscillations in the streamwise velocity were observed due to these flow structures, which may increase fatigue or induce high amplitude motion on downstream turbines. The number of vortices that interact, as other qualitative phenomena of the numerical simulation, were well predicted by a simple stability model of two-dimensional row of vortices. The disturbances imposed by the heave motion were also compared to the eigenvectors resulting from linear stability theory for helical vortices and the predicted growth rates for the wavenumbers resulting from this comparison were consistent with the model of a row of vortices. These results motivate further studies to understand the impact of the larger flow structures on downstream turbines.

The hydrodynamic stability of a vortex system behind two in-line wind turbines operating at low tip-speed ratios is investigated using the actuator-line method in conjunction with the spectral-element flow solver Nek5000. To this end, a simplified setup with two identical wind turbine geometries rotating at the same tip-speed ratio is simulated and compared with a single turbine wake. Using the rotating frame of reference, a steady solution is obtained, which serves as a base state to study the growth mechanisms of induced perturbations to the system. It is shown that, already in the steady state, the tip vortices of the two turbines interact with each other, exhibiting the so-called overtaking phenomenon. Hereby, the tip vortices of the upstream turbine overtake those of the downstream turbine repeatedly. By applying targeted harmonic excitations at the upstream turbine’s blade tips a variety of modes are excited and grow with downstream distance. Dynamic mode decomposition of this perturbed flow field showed that the unstable out-of-phase mode is dominant, both with and without the presence of the second turbine. The perturbations of the upstream turbine’s helical vortex system led to the destabilization of the tip vortices shed by the downstream turbine. Two distinct mechanisms were observed: for certain frequencies the downstream turbine’s vortices oscillate in phase with the vortex system of the upstream turbine while for other frequencies a clear out-of-phase behaviour is observed. Further, short-wave instabilities were shown to grow in the numerical simulations, similar to existing experimental studies [1].