## 3 Results and Discussion
### Comparison of Speed-ups for Horizontal Wind  
Figure 14 shows the results of speed-up in the previous studies, along with the present results. Except for the field test results presented by [PERSON] et al. [5], the curves provided in different studies are for the hill with a shape function of sine/cosine type. It is found that the present results are close to those obtained by [PERSON] et al. [25], for the vertical profile at the hill foot on the upstream side of the hill. However, the greater amounts found in the present study may be attributed to the greater slope used in their work, which slows down the oncoming flow. On the hill crest, the speed-up usually reaches its maximum values. The comparison of the CFD results obtained by [PERSON] and [PERSON] [11] and [PERSON] et al. [29] shows that the speed-up ratio at the same non-dimensional height increases with the increasing \(H\)/\(L\). It is found that the CFD results are generally greater than those obtained from the wind tunnel test and field testing. This may be attributed to the characteristics of the 3-D flow, that is to say the 3-D vortex and separation of the flow lead to a more diffusion/dissipation of the wind energy, in comparison with a 2-D flow. In addition, it is found the present results (\(H\)/\(L\) = 0.286) are close to those obtained in the field measuring (\(H\)/\(L\) = 0.26) [5]. Generally, at the hill foot on the upstream side, the profiles resulting from the 3-D study are greater than those obtained in the 2-D study, whereas the profiles at the hill crest for a hill of 3-D is smaller than that for a 2-D hill. Figure 14: Comparison of speed-up \(S_{u}\) between tests and other studies. Figure 13: The vertical turbulence intensity at different heights. In the following, the present speed-up results are compared with those used in the design codes to further enrich the database of the study on speed-up. The height variation coefficient of wind pressure is defined in GB 50009-2012 [27] to account for the influence of hilly terrain, which is called the terrain correction coefficient \(\eta\). The expression of the correction coefficient \(\eta_{B}\) at the hill crest is  
\[\eta_{B}=\left[1+\kappa\cdot\tan\alpha(1-\frac{z}{2.5H})\right]^{2} \tag{6}\]  
where the term of \(\tan\alpha\) is the slope of the upstream side of a hill/slope, and it is no more than 0.3; \(\kappa\) is a constant (2.2 for a hill and 1.4 for a slope); \(H\) is the height of the hill or the slope; and \(z\) is the height from the hill surface. Furthermore, the wind speed-up caused by hilly terrain is equal to \(\eta_{B}\)\({}^{0.5}\). In ASCE 7-10 [30], the multiplier, \(K_{zt}\), is used to take into account the effects of topography, and is defined as [30]  
\[K_{zt}=(1+K_{1}K_{2}K_{3})^{2} \tag{7}\]  
where \(K_{1}\), \(K_{2}\), and \(K_{3}\) are the factors to consider the reductions in speed-up with horizontal distance downstream and upstream of the crest, and the reduction caused by the height above the local terrain, respectively. Then, the basic wind speed should be multiplied by \(K_{zt}^{0.5}\). The values of \(K_{1}\) for different topographies, such as 2-D hills, and 3-D axis-symmetrical hills, are given by ASCE 7-10. The factors, \(K_{2}\) and \(K_{3}\), can be computed by [30]  
\[K_{2}=(1-|x|/\mu L_{u}) \tag{8a}\] \[K_{3}=\exp(-\gamma z/\mu L_{u}) \tag{8b}\]  
where \(\mu\) and \(\gamma\) are the factors for horizontal and height attenuation, respectively. \(L_{u}\) is the horizontal distance from the hill crest to the upstream slope at 1/2 of the hill height. In the European standard, EN 2004-1-4 [31], the orographic factor \(C_{0}\) is used to account for isolated hills and cliffs, but not for the undulating and mountainous regions, and indicates the increase in mean wind speed. It can be computed by [31]  
\[C_{0}=1\quad\text{for}\quad\phi<0.05 \tag{9a}\] \[C_{0}=1+2s\phi\quad\text{for}\quad 0.05<\phi<0.3\] (9b) \[C_{0}=1+0.6s\phi\quad\text{for}\quad\phi>0.3 \tag{9c}\]  
where \(\phi\) is the upstream slope, and \(s\) is the orographic location factor.