## 5 Conclusions  
This study experimentally investigated the backflow patterns around a groin pair deployed at both banks with different spacing using PIV measurements and compared with the backflow pattern of a single groin.  
For the short groin models used in the present experiment, the length and width of the recirculation zone behind a single groin are approximately 5 and 1.3 times the groin length, respectively. When two groins are symmetrically installed at both banks, the contraction caused by the groins increases the velocity in the main channel through the groin tips. As a result, the recirculation zone of symmetrical groins is slightly shorter than that of a single groin. When two groins are placed alternately, the backflow pattern behind Groin A presents three variation trends responding to the location of Groin B, which is characterized by a critical spacing equal to the groin length, i.e., 5 cm in the present study. Specifically, with the increase in spacing between groins over 5 cm, an upstream alternating Groin B promotes the development of the recirculation zone behind Groin A, whereas a downstream alternating Groin B inhibits the generation and propagation of reversing flow induced by Groin A. It implies that the threshold behavior of backflow patterns depends on the ratio of spacing between two groins to groin length in the alternate layout of short groins. For the short groin used in the study, the threshold value of the ratio is one.  
Spanwise velocity near the groin tip, which is also located in the shear layer zone (0.089 m/s \(\geq v_{xy}\geq 0.030\) m/s), was fitted as linearly related to the width of recirculation zone via correlation analysis. The spanwise velocity has a dominant effect on the width of the downstream recirculation zone from the angular performance of streamline curvature. Additionally, the variation of groin-induced vorticity and recirculation zone length remains almost constant with different spacing between groins.  
Based on momentum conservation, considering and correcting the contraction ratio of cross-section between groins at both banks, dimensionless empirical formulas estimating the recirculation zone length of alternating groins are, respectively, derived corresponding to different spacing between groins. The coefficient of determination \(R^{2}\) is over 0.99. It implies the results from the updated empirical formula can be considered conservative, first-order estimates of the recirculation length formed behind short groins placed in an alternating configuration.  
This study enriches the knowledge on backflow features of two alternating groins with various spacing, which provides a scientific reference to assess the cumulative effect of a groin group in a natural river system. In addition, these findings will be useful for cost-effective configuration of short groins at both riverbanks with respect to optimizing navigation and flood prevention.  
Methodology, C.K., Y.Z., J.G.; formal analysis, C.K., Y.Z. and J.G.; investigation, Y.Z., J.G.; resources, J.G.; data curation, J.G.; visualization, Y.Z., X.H.; supervision, C.K.,J.G.; writing--original draft preparation, C.K., Y.Z.; writing--review and editing, C.K., Q.Z.; project administration, C.K.; funding acquisition, C.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 41776098 and 41976159 and the National Key Research and Development Project of China, grant number 2019 YFC1407900. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data will be available under request to authors. Conflicts of Interest: The authors declare no conflict of interest.