**6. Conclusions**

In this work, we evaluate the capability of an actuator disk model in predicting the wake dynamics of a utility-scale wind turbine by comparing its results with those from an actuator surface model. In the AD model, the same thrust coefficient as that in the AS model is employed. A nacelle model is incorporated into both models. Turbulent flows are simulated using LES with the same mesh and time step for both AD and AS cases. Two inflow conditions are considered, i.e., a uniform inflow and a fully developed turbulent inflow. The wakes computed using the AD model is compared with that from the AS model via the time-averaged field and the DMD analysis. It is found that time-averaged velocity and turbulence kinetic energy computed by the AD model are significantly different from those computed by the AS model until nine turbine rotor diameters downstream for the uniform inflow condition; for fully developed turbulent inflow, the differences between the two models are less significant and agree with each other from seven turbine rotor diameters downstream. The DMD analysis of the uniform inflow cases shows that the vortex shed behind the nacelle triggers the shear layer instabilities on the wake boundary behind both models but of different spatial scales. With a thinner shear layer, the wake predicted by the AD model contains smaller spatial scale oscillations at higher frequency. For the fully developed turbulent cases, the DMD analysis shows that the spectra of both models shift to a lower frequency range and the coherent structures also increase in size. The DMD analysis also reveals significant differences between the two models in the far wake: a bluff-body vortex shedding pattern at *St* = 0.17 appears uniquely in the wake of the AD model as the most dominant DMD mode, whereas the wake computed by the AS model has the most dominant DMD mode of lower energy and at lower frequency *St* = 0.08 which is related to the passive transport by the inflow turbulence large eddies, and with the second dominant mode at a frequency *St* = 0.23 close to the bluff body vortex shedding frequency. It is concluded that the dynamic coherent structures in the wake predicted by the AD model are significantly different from those predicted by the AS models and shall be used with more attention when the dynamics of the wake are of interest. In the present work, the thrust coefficient employed in the AD model is the same as that computed by the AS model. However, since the blade rotation is not modeled in the current AD model, the power coefficient from the AD model is not exactly the same as that from the AS model (the *CP* from the AD is approximately 5% to 10% higher). In the current AD model, the thrust coefficient and the power coefficient cannot be specified at the same time. Further studies on how the differences in the power coefficient affect wake evolutions will be carried out using more advanced AD models considering the effect of blade rotation (e.g., [20]).

**Author Contributions:** Conceptualization, investigation, writing—original draft preparation, Z.L.; conceptualization, methodology, software and writing—review and editing, X.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is partially supported by NSFC Basic Science Center Program for "Multiscale Problems in Nonlinear Mechanics" (NO. 11988102).

**Conflicts of Interest:** The authors declare no conflict of interest.
