**4. Results**

In this section, the simulation results are presented. The uniform inflow cases are presented in the first place and are followed by the turbulent inflow simulations. For each inflow condition, we compare instantaneous flow fields, time-averaged flow fields and DMD modes from the AD simulations with those from the AS simulations. In this section, *u*, *v*, *w* denote the instantaneous flow velocity in the streamwise, spanwise and vertical direction, respectively, with *U*, *V*, *W* for the time-averaged values.

#### *4.1. Uniform Inflow*

## 4.1.1. Instantaneous Flow Field

Figure 2 depicts the simulated instantaneous velocity fields behind the AD and the AS wind turbine models on the *z* = *z*hub plane. For the streamwise velocity contour in Figure 2a,b, it is found that both wake boundaries are first stable in a small distance behind the turbine and then show fluctuations in the far wake. Inside the wake away from the nacelle, the velocity deficit behind the AD model is more evenly distributed along the radial direction than the AS model, since the tip and the root losses and the radial variation of blade sections are not considered in the AD model. In the hub region, the wake of the nacelle is observed in both models. However, a jet which encompasses the nacelle's wake appears uniquely behind the AS model. Figure 2c,d show the spanwise velocity field. Fluctuations appear behind both wind turbine models. In the near wake region, a Kármán vortex street pattern is observed in the centerline of the near wake due to the nacelle. A significant discrepancy emerges in 2 < *x*/*D* < 3 region, where the AD model's result shows a regularly oscillating pattern on

the wake boundary as observed for both streamwise and spanwise velocities (Figure 2a,c). It is also noticed that the spanwise velocity fluctuations in this region are stronger near the wake boundary than those in the wake center. In contrast, the wake behind the AS model does not have this oscillatory boundary, and the vortex shed from the nacelle grows gradually and starts to influence the wake boundary at *x* ≈ 4*D*. In the far wake (*x* > 6*D*), the spanwise velocity behind the AS model seems to be more energetic than that of the AD model. Quantitative comparisons shall be conducted in the next section to confirm this observation.

**Figure 2.** Uniform inflow: contours of the instantaneous velocity field behind the wind turbine on the horizontal plane at hub height. (**a**) streamwise velocity using AD; (**b**) streamwise velocity using AS; (**c**) spanwise velocity using AD; (**d**) spanwise velocity using AS. The solid black line at *x* = 0 illustrates the location and the diameter of the wind turbine.
