# Wind Tunnel Measurements of Surface Shear Stress on an Isolated Dune Downwind a Bridge
## 3 Results  
### Changes in Averaged Surface Shear Stress  
Figure 5 shows the spatial variability of the mean value of normalized surface shear stress (\(\tau^{\prime}\)) on the sand dune and downstream it. The windward slope, leeward slope and the crest of the sand dune can be easily recognized in the graphs. It should be noted that for saving the space, the distance between the bridge and the sand dune, S, in the graphs was not in actual scale. Figure 5a shows that in the isolated dune case, wall shear stress increased on the windward slope compared with that on the flat surface. Near the crest of the windward slope, \(\tau^{\prime}\) was the highest and equals 1.5. In addition, a zone with negative \(\tau^{\prime}\) was formed between x = 2.5 H and 10 H, corresponding to the backward velocity of the airflow (reattachment region was marked in Figure 5a with green lines). When x reaches 20 H, the magnitude of \(\tau^{\prime}\) approaches 0, indicating that wall shear stress was no more affected by the sand dune. In Figure 5b-f, although bridge reduces wall shear stress on the windward slope, the magnitude of \(\tau^{\prime}\) on the windward crest was still high (ranges from 1.25 to 1.5). Moreover, the bridge did not affect the shear stress on the leeward slope dramatically, that is, the change of shear stress on the leeward slope was no more than 5% compared with the isolated case at the same positions. In the cases of S = 1.5 H, 3.0 H and 5.0 H, wall shear stress between x = 5 H and 10 H is affected by the bridge pier and desk. That is, the wall shear stress measured at 5 H \(<\) x \(<\) 10 H, y = L/2 is higher than that measured at 5 H \(<\) x \(<\) 10 H, y = 0. Moreover, wall shear stress downwind the sand dune is not affected by the bridge in the case of S = 10.0 H and 20.0 H.  
To analyze the change of normalized surface shear stress quantitatively, Figure 6 shows normalized surface shear stress (\(\tau^{\prime}\)) as a function of the interval distance (\(S\)) and stream-wise position. Figure 6a shows the variation of the normalized surface shear stress (\(\tau^{\prime}\)) along the centerline (\(y\) = 0). Compared with the isolated dune case, the surface shear stress on the windward slope was reduced due to shelter of the pier (except at the two points at the beginning of the windward slope). When the free-stream wind velocity \(u_{0}\) was 15 m s\({}^{-1}\), the \(\tau^{\prime}\) on the windward crest decreased by 20.4%, 28.2%, 31.7%, 6.4% and 0.5%, corresponding to the cases of S = 1.5 H, 3.0 H, 5.0 H, 10.0 H and 20.0 H respectively. In the case that S equals 20.0 H, the shelter effect of the wall shear stress almost disappears. The shelter region length of the wall shear stress is between 10 and 20 times the bridge height, which is longer than that of a cylinder. We attribute this to the coeffects from the bridge pier and desk. Figure 6b shows the variation of the normalized surface shear stress (\(\tau^{\prime}\)) along y = L/2 with the free-stream wind velocity \(u_{0}\) = 15 m/s. Compared with the isolated dune case, shear stress on the crest decreases by 11.4%, 9.1%, 12.0%, 0.5% and \(-\)2.3%, corresponding to the cases of S = 1.5 H, 3.0 H, 5.0 H, 10.0 H and 20.0 H. In the downwind area of the sand dune, the shear stress shows some increase from x = 2.5 H to 15 H compared with the isolated dune case. At the downstream position of x = 20 H, the shear stress became stable and almost equal