Laboratory experiments have yielded evidence suggestive of large-scale meandering motions in the wake of an axial flow hydrokinetic turbine in a turbulent open channel flow (Chamorro et al., J. Fluid Mech., vol. 716, 2013, pp. 658–670). We carry out a large-eddy simulation (LES) of the experimental flow to investigate the structure of turbulence in the wake of the turbine and elucidate the mechanism that gives rise to wake meandering. All geometrical details of the turbine structure are taken into account in the simulation using the curvilinear immersed boundary LES method with wall modelling (Kang et al., Adv. Water Resour., vol. 34(1), 2011, pp. 98–113). The simulated flow fields are in good agreement with the experimental measurements and confirm the theoretical model of turbine wakes (Joukowski, Tr. Otdel. Fizich. Nauk Obshch. Lyub. Estestv., vol. 16, 1912, no. 1), yielding a near-turbine wake that consists of two layers: the tip vortex (or outer) shear layer that rotates in the same direction as the rotor; and the inner layer counter-rotating hub vortex. Analysis of the calculated instantaneous flow fields reveals that the hub vortex undergoes spiral vortex breakdown and precesses slowly in the direction opposite to the turbine rotation. The precessing vortex core remains coherent for three to four rotor diameters, expands radially outwards, and intercepts the outer shear layer at approximately the location where wake meandering is initiated. The wake meandering manifests itself in terms of an elongated region of increased turbulence kinetic energy and Reynolds shear stress across the top tip wake boundary. The interaction of the outer region of the flow with the precessing hub vortex also causes the rotational component of the wake to decay completely at approximately the location where the wake begins to meander (four rotor diameters downstream of the turbine). To further investigate the importance of turbine geometry on far-wake dynamics, we carry out LES under the same flow conditions but using actuator disk and actuator line parametrizations of the turbine. While both actuator approaches yield a meandering wake, the actuator line model yields results that are in better overall agreement with the measurements. However, comparisons between the actuator line and the turbine-resolving LES reveal significant differences. Namely, in the actuator line LES model: (i) the hub vortex does not develop spiral instability and remains stable and columnar without ever intercepting the outer shear layer; (ii) wake rotation persists for much longer distance downstream than in the turbine-resolving LES; and (iii) the level of turbulence kinetic energy within and the overall size of the far-wake meandering region are considerably smaller (this discrepancy is even more pronounced for the actuator disk LES case) compared with the turbine-resolving LES. Our results identify for the first time the instability mechanism that amplified wake meandering in the experiment of Chamorro et al., show that computational models that do not take into account the geometrical details of the turbine cannot capture such phenomena, and point to the potential significance of the near-hub rotor design as a means for suppressing the instability of the hub vortex and diminishing the extent and intensity of the far-wake meandering region.

We study the turbine spacing effects in infinite, aligned wind-turbine arrays using large-eddy simulation (LES) with the wind turbine rotors parameterized as actuator disks. A series of simulations is carried out to systematically investigate the different effects of streamwise and spanwise turbine spacings on the array power output and turbulence intensities. We show that for the same turbine density, increasing the streamwise spacing is more beneficial than increasing the spanwise spacing. Larger streamwise turbine spacing increases the power extraction and lowers the turbulence intensity at each turbine more efficiently than when the spanwise turbine spacing is increased. The reason for the different effects of streamwise and spanwise turbine spacings on wind farm performance is that the wake recovery of wind turbines in infinite arrays depends on the area influenced by the wind-turbine wakes, rather than the land area occupied by each turbine. Based on this idea, an improved effective roughness height model is proposed, which can account for the different effects of streamwise and spanwise turbine spacings in infinite aligned wind farms. The predictive capabilities of the new model are demonstrated via extensive comparisons with results obtained from the LES and previously proposed roughness height models.

Wind turbine wakes, being convectively unstable, may behave as an amplifier of upstream perturbations and make downstream turbines experience strong inflow fluctuations. In this work, we investigate the effects of the side-to-side motion of a floating offshore wind turbine (FOWT) on wake dynamics using large-eddy simulation and linear stability analysis (LSA). When the inflow turbulence intensity is low, simulation results reveal that the turbine motion with certain Strouhal numbers $St = fD/U_\infty \in (0.2,0.6)$ (where $f$ is the motion frequency, $D$ is the rotor diameter, and $U_\infty$ is the incoming wind speed), which overlap with the Strouhal numbers of wake meandering induced by the shear layer instability, can lead to wake meandering with amplitudes being one order of magnitude larger than the FOWT motion for the most unstable frequency. For high inflow turbulence intensity, on the other hand, the onset of wake meandering is dominated by the inflow turbulence. The probability density function of the spanwise instantaneous wake centres is observed being non-Gaussian and closely related to that of the side-to-side motion. This complements the existing wake meandering mechanisms, that the side-to-side motion of an FOWT can be a novel origin for the onset of wake meandering. It is also found that LSA can predict the least stable frequencies and the amplification factor with acceptable accuracy for motion amplitude $0.01D$ . Effects of nonlinearity are observed when motion amplitude increases to $0.04D$ , for which the most unstable turbine oscillations shift slightly to lower frequencies and the amplification factor decreases.