# Wind Tunnel Measurements of Surface Shear Stress on an Isolated Dune Downwind a Bridge
## 5 Conclusions  
We used 34 Irwin sensors to measure the surface shear stress on a sand dune model that is downstream a bridge model immersed in a fully developed turbulent boundary layer in a wind tunnel. The results showed that the averaged wall shear stress on the windward crest of the sand dune is decreased by the bridge in the cases of S = 1.5 H, 3.0 H and 5.0 H. The decrease ratio obtained at y = 0 is greater than that obtained at y = L/2.  
The bridge also affected the fluctuation of surface shear stress on the sand dune. In the case of S = 1.5 H, 3.0 H and 5.0 H, the fluctuation of surface shear stress at the windward crests decreased at y = 0 and is increased at y = L/2 compared with the isolated dune case. Downstream the sand dune, the restraint effect of the bridge pier on the wall shear fluctuation is greater than that of the bridge desk.  
The fraction time parameter \(\psi\) used in the study to assess the local dominance of erosion and deposition mechanisms indicated strong erosion on the windward slope. The value of \(\psi\) increases with height on the windward slope of an isolated sand dune. However, in the cases of S = 1.5 H, \(\psi\) is decreased by the bridge in the lower part of the sand dune at y = 0 and is increased at y = L/2 compared with the isolated dune case. In other cases, the change of \(\psi\) on the windward slope is not as prominent as in the case of S = 1.5 H. Downstream the sand dune, erosion starts in a point between x = 10 H and 15 H in all cases. However, differences in the value of \(\psi\) downwind the sand dune indicates the erosion rate can be different.  
Figure 8: Fraction time threshold time parameter \(\psi\) with normalized distance x/H. H is the height of sand dune, L is the distance of pairs of bridge, S is the distance between bridge and sand dune and y is the distance between measuring position and the y-axis.  
Last to be acknowledged, wind tunnel experiments of geometrically similar models cannot fulfill the Reynolds similarity. To get more precise results, the next study we concentrate on the field observation of shear stress and sand flux so that erosion patterns on the sand dune downstream a bridge. The simple assumption in this paper will be improved.  
Conceptualization, H.D. and N.H.; methodology, W.H.; investigation, W.W. and H.D.; resources, N.H.; data curation, W.W. and W.H.; writing--original draft preparation, W.W. and W.H.; writing--review and editing, H.D.; funding acquisition, N.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National key research and development projects (2016 YFC0500901). National natural science foundation of China (11772143), Scientific and Technological Services Network Planning Project of Cold and Arid Regions Environmental and Engineering Research Institute, CAS (HHS-TSS-STS-1504), Central university fund (lzujbky-2020-cd06).  
The authors would like to thank [PERSON], Lanzhou University, for the constructive suggestions.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.