## 3 Results
### Horizontal Flow Patterns
#### 3.1.2 Flow Fields of Two Alternating Groins with Various Spacing  
Figure 6 shows the time-averaged horizontal streamlines behind Groin A that are affected by Groin B located at the opposite bank with 5-, 15-, 25-, 35-, 45-, and 55-cm spacings upstream and downstream from Groin A. When Groin B is upstream from Groin A, the flow reattachment point of Groin A moves further downstream with increasing  
Figure 4: Time-averaged velocity distribution and streamlines of (**a**) a single Groin A and (**b**) two symmetrical Groins A and B: the color indicates the velocity magnitude. Figure 5: Schematic diagram of streamlines and observed points of velocities on the cross-section through the groin tip for the single groin (solid line) and symmetrical groins (dotted line), in which \(b_{max}\) indicates the backflow width and \(L\) represents backflow length (top view). spacing between groins, as shown in the left column of Figure 6. Likewise, the flow fields near Groin A with Groin B downstream, shown in the right column of Figure 6, indicate that the recirculation zone behind Groin A is significantly smaller than that with Groin B upstream. As a consequence, a smaller low-velocity zone was formed behind Groin A. To quantify the evolution of backflow patterns behind Groin A with different spacings between the two groins, the main characteristic parameters of the recirculation zone behind Groin A are calculated and are listed in Table 1 for all test cases. The length and width of the recirculation zone are normalized by groin length b, as L/b and B/b, respectively. The width of the recirculation zone was expected to increase with increasing recirculation length. In the case of Groin B upstream from Groin A, the recirculation zone behind Groin A becomes larger than that without Groin B (namely Case 14, a single groin). The longest recirculation zone behind Groin A occurred during Case 5, where Groin B was located 0.15 m upstream from Groin A; the backflow streamwise length was over 50% more than that behind the single groin during Case 14. In contrast, when Groin B was deployed downstream from Groin A, the backflow size behind Groin A was smaller than that of a single groin. The recirculation zone behind Groin A reached a minimum when Groin B was 0.15 m downstream from Groin A (Case 9), where the recirculation length was more than 30% less than that behind a single groin. These results indicate that an upstream alternating Groin B promotes the development of a recirculation zone behind Groin A, whereas a downstream alternating Groin B inhibits the generation and propagation of reversing flow induced by Groin A. The normalized length and width of the recirculation zone behind Groin A are shown in Figure 7. The variation of recirculation zone length can be divided into three subzones. First, Cases 1-5 are classified as upstream far-field. As Groin B moves toward Groin A, the main channel becomes narrower; therefore, the velocity is larger and the low-velocity zone at Groin B is expanded. The recirculation zone behind Groin A is lengthened from 0.314 to 0.384 m, about 20%. Second, Cases 6-8 are classified as the upstream and downstream near-field and symmetrical layout. The width of the channel between the groins was narrowed remarkably in these three cases, and the low-velocity zone near the groins reached the maximum for the symmetrical groin layout. The main channel was separated by groin tips and the fluid stream spread rapidly after bypassing Groin B due to fluid inertia, which significantly inhibited the backflow induced by Groin A. As a result, the recirculation zone behind Groin A was shortened from 0.35 to 0.17 m, about 50%. Third, Cases 10-13 are categorized as the downstream far-fields. As Groin B moves downstream far away from Groin A, the main channel next to Groin A was narrowed less and the low-velocity area at the opposite bank also became smaller than the other two subzones. Thus, the upstream fluid was mainly affected by the incoming flow.