## 3 Results
### Velocity along Cross-Section through Groin Tip and Its Influence on Recirculation Zone  
The flow field near a groin has a dominant effect on the backflow pattern behind the groin. Because the velocity near the groin tip is directly associated with the downstream turbulent intensity and the streamwise propagation of recirculating flow. Therefore, the time-averaged streamwise and spanwise velocity components at 19 points evenly distributed along the cross-section of the groin tip were extracted to examine their influence on the downstream recirculation. The schematic of observed points at the cross-section of a single groin is plotted in Figure 5; the positions of velocity observation points in the other cases of alternating groins are the same, except with only 17 points extracted for the symmetrical groins. Figure 9 shows the time-averaged streamwise velocity component (i.e., \(x\)-velocity, \(v_{x}\)) of each observed point on the cross-section of Groin A. The streamwise velocity at points 1-3 nearest the groin tip and points 16-19 nearest the opposite bank varied markedly; however, at points 4-15 in the middle of the main channel it was hardly changed. The streamwise velocity reached the maximum near the fourth point in front of the groin, except for Case 7 (symmetrical groins), where the maximum velocity appears at the fifteenth point due to the other groin symmetrically deployed at the opposite bank, see Figure 9. Overall, the variation time-averaged streamwise velocities at points 1-3 were similar to each other, i.e., the velocity linearly increased from point 1 to 3 due to the strong shear stress near the groin wall. However, the streamwise velocity at points 16-19 decreased and the variation of each case varied notably, which implies that streamwise velocity at the opposite bank is not simply affected by the contacted section of groin but also by the flume wall. The streamwise velocity represents the water flux through the cross-section of the main channel, and plays a leading role on the flow structure near Groin A and further alters the backflow induced by the groin. The averaged streamwise velocity of points 16-19 (denoted as \(\overline{v_{x,16-19}}\)) for each case and the length of the recirculation zone are correspondingly presented in Figure 10, in which the negative value of spacing between groins represents Groin B located upstream of Groin A. It is obvious that \(\overline{v_{x,16-19}}\) had completely different properties with various locations of Groin B. When Groin B was located in the upstream far-field and moves towards Groin A (Cases 1-5), with shorter spacing between groins, the streamwise velocity gradually decreased because the upstream cross-section of Groin A contracted continuously, so that the length of the recirculation zone behind Groin A progressively increased. In particular,  
Figure 8: Relationship between the recirculation length behind Groin A (\(L\)) and the spacing between groins (\(x\)) for cases 1–5 and cases 9–13, respectively. the minimum of \(\overline{v_{x},16-19}\) and the maximum of backflow length appeared in Case 5, in which the spacing between groins was 0.15 m. When Groin B was deployed in the near-field (Cases 6-8) since groins too close to one another will prevent flow reattachment, keeping the shear stress between groins rather low, the change of streamwise velocity varied and the backflow length rapidly decreased the in above three cases. As Groin B was placed in the downstream far-field (Cases 9-13), \(\overline{v_{x},16-19}\) and recirculation length gently increased again because the narrowed cross-section was gradually wider with Groin B away from Groin A.  
Figure 9: Time-averaged streamwise velocity (\(\overline{v_{x}}\)) at the observed points along the cross-section located at Groin A tip for (**a**) single groin and Groin B located at upstream of Groin A; (**b**) symmetrical groins and Groin B located downstream of Groin A.