# Experimental Study of Downburst Wind Flow over a Typical Three-Dimensional Hill
## 3 Results and Discussion
### Comparison with the Results of Previous Studies  
Since the results of previous studies mainly pertain to horizontal wind dynamics, this section focuses only on the comparison of the horizontal wind velocities. Regarding the hill models located in the strong horizontal wind region, the maximum \(M_{\rm t,max}\) for each model and hill position are summarized in Table 4. The maximum \(M_{\rm t,max}\) shown in the table could aid in determining downburst wind loads and inform a simplified design of structures subjected to such conditions. It is evident that both the maximum \(M_{\rm t,max}\) obtained at the crest and that observed at the hill foot decreased with the increase in the hill height. In addition, the maximums of \(M_{\rm t,max}\) obtained elsewhere were relatively large, in the range of 1.03 to 1.12. Note that the work by [PERSON] et al. [22], utilizing a hill model with a similar shape to those employed in the present study, found that the maximum speed-up ratio during an ABL wind flow over a 3D hill was about 1.34. It can be thus concluded that the speed-up effect found during a downburst wind is commonly smaller than occurs during an ABL wind, provided the hill terrain is the same. This is consistent with the findings of previous studies [6,7]. The Australian and New Zealand standard entitled \"Overhead line design--detailed procedures\" (AS/NZS 7000: 2010) [29] specifies that the topographical multiplier \(M_{\rm t,downdraft}\) for downbursts can be computed using the formula  
\[M_{\rm t,\ downdhurst}=0.5+0.5M_{\rm t,\ synoptic} \tag{3}\]  
where \(M_{\rm t,synoptic}\) is the topographical multiplier for synoptic winds and is defined in the code entitled \"Structural design actions-Part 2: wind actions\" (AS/NZS 1170.2: 2011) [30]. For the present study, \(M_{\rm t,synoptic}=M_{\rm h}\), where \(M_{\rm h}\) is the hill shape multiplier specified in AS/NZS 1170.2: 2011 [30] and can be computed using the formula  
\[M_{\rm h}=\left\{ \begin{array}{ll}1,&\phi<0.05\\ 1+(\frac{H}{3.5(2+L_{1})})(1-\frac{|x|}{L_{2}}),&0.05\leq\phi\leq 0.45\\ 1+0.71(1-\frac{|x|}{L_{2}}),&\phi>0.45\ {\rm and}\ x\in[0,\ \frac{H}{4}]\\ 1+(\frac{H}{3.5(2+L_{1})})(1-\frac{|x|}{L_{2}}),&\phi>0.45\ {\rm and}\ x\
otin[0,\ \frac{H}{4}]\end{array} \right. \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{10}{c}{**Hill Models**} \\ \cline{2-13}  & **H1** & **H2** & **H3** & **H4** & **H5** & **H6** & **H7** & **H8** & **H9** & **H10** & **H11** & **H12** \\ \hline \multirow{2}{*}{\begin{tabular}{c} Crest \\ Hill foot \\ Else \\ \end{tabular} } & 1.07 & 0.88 & 0.56 & 0.41 & 0.28 & 0.21 & 0.98 & 0.92 & 0.66 & 0.44 & 0.30 & 0.23 \\ \multirow{2}{*}{\
\begin{tabular}{c} Hill foot \\ Else \\ \end{tabular} } & 1.04 & 1.04 & 1.04 & 1.04 & 1.06 & 1.06 & 0.97 & 0.98 & 0.96 & 0.96 & 0.96 & 0.95 \\ \multirow{2}{*}{
\begin{tabular}{c} Else \\ \end{tabular} } & 1.08 & 1.07 & 1.03 & 1.03 & 1.04 & 0.97 & 1.05 & 1.11 & 1.06 & 1.06 & 1.12 & 1.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum of \(M_{\rm t,max}\) for hill models. where \(L_{1}\) and \(L_{2}=4L_{1}\) are the length scales used to determine the vertical and the horizontal variations in \(M_{\rm h}\), and \(L_{1}\) can be taken as the greater of \(0.36L_{\rm u}\) or \(0.4H\). For the \(M_{\rm t,max}\) at the crest, Figure 24 shows the results from the previous research, the curves defined using Equation (3), and the experimental results from the present study. It can be observed that in the case of a small slope (\(\phi\leq 0.45\)) the results show good agreement. With the increase in the slope, the \(M_{\rm t,max}\) at the crest decreases, whereas AS/NZS 7000: 2010 [29] merely provides a constant topographic multiplier, which results in an excessively conservative design in general. There is a need for formulas that enable a relatively accurate prediction of \(M_{\rm t,max}\) in order to inform a rational design of structures. The discrepancy is largely attributable to the confined nature of the downburst.