# Numerical Study on Tree Belt Impact on Wind Shear on Agricultural Land
## 3 Results  
The flow is influenced by the porous drag of the tree belt, but also by the skin friction with the ground. Wall functions play a vital role in determining the latter and its influence on the velocity profiles in the vertical direction. Standard wall functions were first attempted but they failed to predict the ground friction correctly under atmospheric flows. Figure 4 compares the predicted profiles of standard and atmospheric wall functions several hundred meters from the inlet in the absence of a tree belt. It is clear that the latter agreed practically completely with the logarithmic profile. There was some discrepancy in the lower heights, which can be attributed to the function model, or to the bit higher dimensionless wall distance, which rose from 70 to 170 on average after application of atmospheric wall functions. Yet this discrepancy, especially compared to standard wall functions, was marginal. Three values of tree belt porosity were studied, giving rise to the velocity distributions in the central streamwise plane, as shown in Figure 5. The slow-down downstream of the belt became more clearly visible at porosity of 0.5 m\({}^{-1}\). The wake thickness increased and approached the size of wake behind a solid body. Thus, for porosity coefficients above 0.5-1 m\({}^{-1}\), little change is to be expected. It is worth mentioning that at higher-porosity drag, the flow above the belt accelerated in order to fulfill continuity. This can have implications for the operation of wind turbines in the immediate vicinity of the belt. As the operation of wind turbines is also dependent on turbulence, the turbulent kinetic energy is presented in Figure 6 for the three porosity coefficients. The turbulence generation was mainly in the shear layer created by the belt, which was advected downstream. Here, the influence of belt porosity was clearly visible, both in the intensity and in the size of the influenced zone. For the low-porosity coefficient, the turbulent zone spanned around 1.5 tree belt heights in the vertical direction, and the increase in turbulence can be considered marginal. For the higher-porosity coefficient, the zone spanned around 2.5 tree  
Figure 4: Comparison of standard and atmospheric wall functions. Figure 5: Velocity (m/s) contours in the central streamwise plane with belt porosity coefficients of 0.1 m\({}^{-1}\) **(top)**, 0.2 m\({}^{-1}\) **(middle)**, and 0.5 m\({}^{-1}\) **(bottom)**. heights, and the increase in turbulence was 2-3-fold compared to the flow upstream. The turbulence wake also increased in length, and for higher-porosity coefficients it may require a distance up to 15-20 tree heights (350-500 m) for the effect to practically dissolve. In a next step, the vertical profiles of velocity at selected locations within the central streamwise plane were plotted for different porosity values. Figure 7 shows the case for the lowest porosity coefficient of 0.1 m\({}^{-1}\). The locations have been normalized with the height of the tree belt (h), with zero reference for the streamwise coordinate x taken at the front of the belt. As expected, the velocity behind the belt diminished, as demonstrated by the x = 2 h and x = 5 h profiles. However, the curves also showed that about 1.5 h above ground, the velocity started to increase, compared to the logarithmic atmospheric profile, and this increase gradually diminished until a height of about 150-200 m, where the velocity regained its logarithmic atmospheric layer value. Further downstream, this effect was less pronounced, but could be still witnessed until streamwise locations of 20-50 h. The reason is mass conservation, which increases the airflow above the belt to compensate for the obstructed flow through the belt. The higher the obstruction, the higher the effect on the velocity above the belt. Figure 8 shows the profiles for a porosity of 0.2 m\({}^{-1}\), which confirmed this hypothesis. The velocity deficit downstream of the belt was more pronounced and could be felt further downstream (x = 50 h).