Understanding the wake characteristics of wind turbines under the influence of atmospheric turbulence is crucial for developing advanced turbine control algorithms, such as the coordinated turbine control for improving the performance of the entire wind farm as an integrated system. In this work, we systematically investigate the wake of a utility-scale wind turbine for different thrust coefficients, which is relevant to the coordinated axial induction control. Large-eddy simulation (LES) with novel actuator surface models for turbine blades and nacelle is employed to simulate turbine wakes. Different thrust coefficients are achieved by varying the tip-speed ratio, i.e., $\lambda =6.8,7.8,8.8,9.3$. The inflow is generated from a precursory simulation using a very large computational domain to include the large-scale flow structures in atmospheric turbulence. The computed results show that varying the tip-speed ratio gives rise to differences in wake statistics, such as the wake recovery rate and the turbulence intensity. However, the computed results also reveal similarities in wakes from different tip-speed ratios. It is found that the characteristic velocity defined by the thrust on the rotor scales the turbine-added turbulence kinetic energy computed based on different wake center locations. For all considered tip-speed ratios, two dominant frequencies of the large-scale motion of the wake are observed, one is the dominant low frequency of the large-scale flow structures in the inflow prevailing at almost all downwind locations, the other one is the frequency of Strouhal number about 0.15 prevailing at far wake locations ($>3\sim 4$ rotor diameters). The existence of the inflow frequency in the large-scale motion of wakes shows the effects of incoming large-scale flow structures on wake meandering. The Strouhal number of the second frequency, however, is typical for that of vortex shedding behind bluff bodies. This finding suggests the coexistence of the two mechanisms for wake meandering, i.e., inflow large-scale turbulent flow structures and the wake shear layer instability, with the corresponding motion termed inflow-driven wake meandering and shear-induced wake meandering, respectively. The effects of wake and turbine energy extraction on motion of different frequencies are examined for different tip-speed ratios. As approaching the turbine upwind, the energy of the low-frequency motion of the inflow is significantly attenuated, while the energy of the motion at frequencies higher than the inflow low frequency are observed to increase for most cases. In the near wake, decreases of energy are observed for all the frequencies in almost all the cases. At far wake locations, the energy of the motion at all frequencies is increased to a level higher than that of the inflow (at $2D$ turbine upwind) in almost all the cases. At last, the statistics of wake centers in the spanwise and vertical directions are examined. It is found that the probability density function (PDF) profiles of wake center fluctuations nearly collapse with each other for different tip-speed ratios. The Gaussian distribution is found to be an acceptable approximation for the PDF of wake center locations at near wake locations (e.g., $2D,4D$, and $6D$ turbine downwind), while it is a poor approximation at far wake locations (greater than $8D$ turbine downwind). Downwind variations of the mean values and the standard deviations of wake center fluctuations are also observed to nearly collapse with each other for different tip-speed ratios. The observed similarities of turbine wake statistics illuminate the possibility of developing advanced engineering models taking into account the unsteady features of turbine wakes for advanced turbine controls.

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• Structure & turbulence of boundary layers
• Wakes & jets