**1. Introduction**

Nowadays, large wind farms are constructed to respond to the increasing demand of renewable energy. In these wind farms, turbines are installed in cluster to meet the geographical restriction and to reduce the cable and maintenance cost. A turbine may influence its downwind neighbors significantly with the wake effect, leading to a loss of the power production and an increase of the unsteady load on the structure [1]. Therefore, a need to better understand the wake behavior and its influence on the downwind turbines arises.

Understanding turbine wakes in a wind farm is challenging because of its multi-scale nature. For example, the boundary layer on a wind turbine's blade has a thickness of the centimeters, which is orders of magnitudes smaller than the diameter of the rotor (≈100 m) and the thickness of the Atmospheric Boundary Layer (ABL; ≈1000 m) [2]. Among others, the difficulty in accurately modeling the flow around the blade of a real wind turbine blade arises both in wind tunnel experiments (due to scale effect [3]) and in numerical simulations (due to the resolution requirement).

Facing this challenge, it is often assumed that the actual geometry of the rotor is of less importance [4] if only the far wake and its influence on downwind turbines are of interest, so that the wind turbine can be approximated by equivalent models. In experiments, the simplest model is the porous disk model, which is broadly used [5,6]. Validations in wind tunnels have demonstrated that porous discs can provide time-averaged wake properties with satisfactory accuracy in the region further than 3.5 rotor diameters downstream, especially when the turbulence of the ABL is concerned [7–9].

In numerical simulations, a series of blade approximated actuator type models representing the turbine blades using equivalent distributed forces have been proposed. The way in which these forces are calculated and distributed distinguishes different models. The simplest is the Actuator Disk (AD) model, which is the numerical equivalence of a porous disk. The thrust on the disk is calculated with one-dimensional momentum theory and is usually distributed uniformly over the rotor swept area with the rotation effects neglected. The Actuator Line (AL) method was proposed to take into account the effects of individual rotating blades [10]. The AL models a wind turbine blade by a rotating line with lift and drag forces determined from tabulated geometric and aerodynamic data of airfoil. To better take into account the geometrical effects of wind turbine blades, the Actuator Surface (AS) method has been proposed, which models a blade as a two dimensional surface with zero thickness [11,12]. Because of its simplicity and computational efficiency, the AD has been widely used in turbine wake simulations especially in farm-scale simulations [13–16]. The capability of the actuator disk model in predicting turbine wakes, especially in the far wake region, has been widely validated in the literature [14,17,18]. However, besides the thrust, experiments revealed that the rotor's rotation also influences both the power output and the wake characteristics significantly [19] and including these rotational effects in the actuator disk model can improve the model's accuracy [20]. In [21], the authors showed that the actuator disk model can reasonably predict the mean velocity profiles but underpredict the turbulence kinetic energy (TKE) for the wake of an axial-flow hydrokinetic turbine. It is noticed that most of the validation studies were focused on time-averaged quantities without probing into the dynamic behavior of turbine wakes, e.g., coherent flow structures and the wake meandering, for which the dataset is difficult to obtain from utility-scale wind turbines [22]. Furthermore, inconsistent results were observed in wind tunnel experiments on the dynamic behavior of turbine wakes when different turbine models were used. For instance, regarding the origin of wake meandering, Medici et al. [3,23] found the wake meandering was related to the bluff body vortex shedding in the experiment of a small scale wind turbine, whereas Espana et al. [6] claimed that the meandering was attributed to the inflow large eddies by carrying out an experiment by representing the turbine with a porous disk. These wind tunnel measurements already make it questionable whether the AD (or the porous disk) model can predict correctly the dynamics of small scale wind turbine wakes. Less is known when applying such a model to utility-scale wind turbines.

To this end, the present study employs simulation results from the well-validated AS model proposed in [11] to examine the capability of the AD model in predicting the dynamic behavior of a utility-scale wind turbine under uniform and fully developed turbulent inflow conditions. Large-Eddy Simulation (LES) is employed for turbulent flow simulations. For both models, exactly the same computational setup is employed. We first compare the time-averaged quantities and then employ the dynamic mode decomposition (DMD) to facilitate the comparison of the most dominant dynamic flow structures and the frequency spectra between the AD and AS models.

The remainder of this paper is structured as follows. Section 2 presents the theory of the AD and the AS models together with a brief description of the LES solver and the DMD method. In Section 3 the simulation setup is provided. Section 4 depicts the simulation results and the DMD analysis in both uniform and ABL conditions. A discussion is provided in Section 5 before the final conclusion in Section 6.
