## 4 Application: Windage Yaw of the Jumper Cable over Hilly Terrain
A compromise should be made between the calculation accuracy and the cost. The mesh with 160 elements was therefore adopted in the following FE analysis. With consideration of the disturbance of the hilly terrain to the ABL wind, the corresponding wind-induced structural responses can be obtained through Equations (13)-(16), and denoted as \(R\). Note that the structural response herein can be the translational displacement, windage yaw angle, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Diameter of the cable & 21.6 mm \\ Span of the cable & 12 m \\ Sag of the cable (\(D_{s}\)) & 3.33 m \\ Height of the lowest point of the cable & 30 m \\ Density of the cable & 3176 kg/m\({}^{3}\) \\ Density of the air & 1.25 kg/m\({}^{3}\) \\ \(\mu_{xx}\) and \(\mu_{zz}\) & 1.1 \\ Wind speed at the lowest point (\(V_{0}\)) & 22.82 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculating parameters of the jumper cable. Figure 17: FE model of the jumper cable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Elements** & **20** & **40** & **80** & **160** & **320** \\ \hline streamwise displacement (m) & 2.6357 & 2.6360 & 2.6353 & 2.6352 & 2.6351 \\ vertical displacement (m) & 1.2955 & 1.2960 & 1.2954 & 1.2952 & 1.2952 \\ windage yaw angle (\({}^{\circ}\)) & 52.746 & 52.756 & 52.741 & 52.737 & 52.736 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The wind-induced response with different number of elements. Figure 18: Positions of the jumper cable on the hill. internal force, and so on. For convenience, the wind response accounting for the hilly terrain is normalized by  
\[\overline{R}=R/R_{0} \tag{16}\]  
where \(\overline{R}\) is the normalized wind-induced response, and \(R_{0}\) is the corresponding response resulting from the undisturbed ABL wind. In this study, the streamwise displacement, vertical displacement, and the windage yaw angle of the cable immersed in the undisturbed ABL wind are 1.22 m, 0.23 m, and 11.69\({}^{\circ}\), respectively, given that the wind speed at 30 m height is 22.82 m/s. The normalized wind-induced responses are shown in Figure 19, where only streamwise wind speed is considered. Compared to the wind-induced responses in the undisturbed ABL wind field, at the foot of the upstream and downstream sides of the hill, the wind-induced response of the jumper cable weakens, and the response then increases near the crest. The vertical displacement has a largest increase, which is 90% larger than that in the undisturbed ABL wind field at the hill crest. Because the wind slows down at the foot of the upstream and downstream sides of the hill, as a result the wind loads suffered on the jumper cable reduce. Thus, the streamwise and vertical displacements of the cable decrease, and so does the corresponding windage yaw. Furthermore, the wind speeds up near the hill crest and the phenomenon of wind speed-up is very significant, which leads to the increase of the wind loads imposed on the jumper cable. Consequently, it will cause the increase of the streamwise and vertical displacements, as well as the corresponding windage yaw angle. To study the effects of the vertical wind speed on the wind-induced response of the jumper cable, the wind-induced responses of the jumper cable located on the along-wind center line of the hill (\(y=0\)) are compared. The streamwise displacement, vertical displacement, and windage yaw angle of the lowest point of the jumper cable under different conditions, i.e., considering the vertical wind speed or not, are shown in Table 3. On the upstream side of the hill, the wind-induced responses decrease with \(x\!/\!L\) and then increase, and reach their maximum at the crest (\(x\!/\!L=0\)). After considering the vertical wind speed, the increase of these three wind-induced responses of the jumper cable are remarkable at \(x\!/\!L=-0.5\) and \(x\!/\!L=-0.25\), and the maximum increase of vertical displacement is 9.30%.