4.2.2. Time-Averaged Flow Field

Figure 6 shows the profiles of time-averaged flow quantities. Before the following detailed analysis, it is clear that the results from the AD model are in an overall good agreement in the far wake (*x* > 7*D*) for turbulent inflow condition, in contrast to Figure 3 of the uniform inflow condition. For the streamwise velocity, differences between the AD and the AS models are only observed in the near wake region (*x* < 3*D*) and become insignificant at far wake locations as shown in Figure 6a. The wakes computed by both models slightly skew towards the −*y* direction due to the insufficient simulation time, which causes the inflow not perfectly symmetric with respect to *y* = 0. The spanwise profiles of TKE are shown in Figure 6b. As seen, the TKE is concentrated near the hub (*y* = 0) and the wake boundary (*y* ± 0.5*D*) at *x* = 1*D* with larger TKE near the hub and near the boundary for the AS and AD models, respectively. The region of high TKE increases and expands as the wake travels from (3*D* < *x* < 5*D*) and the TKE computed by the AS model develops faster and surpasses that computed by the AD after (*x* > 3*D*). At further turbine downwind locations, the two models show consistent results. Similar trends are observed for the Reynold's stress <*u*- *v*- > as shown in Figure 6c. In Figure 6d,e, the vertical distribution of streamwise velocity and the turbulence intensity also confirms the above conclusion that the two models agree well in the far wake and the differences only manifest in the near wake region.

To this extend, the AD model can reasonably predict the time-averaged flow quantities in the far wake for turbulent inflow conditions.

**Figure 6.** Turbulent inflow: Horizontal profile of time-averaged (**a**) streamwise velocity, (**b**) turbulence kinetic energy, and (**c**) the primary Reynolds stress <*u*- *v*- > at different downstream location at hub height (*z* = *z*hub); vertical profile of time-averaged (**d**) streamwise velocity and (**e**) turbulence intensity on the plane *y* = 0.
