**5. Discussion and Conclusions**

Bridges with foundations in river beds with supercritical flow regimes are frequent and can be found worldwide. Handling the scouring process that takes place in this type of flow (e.g., with bed sills [106]) is crucial for the structural integrity of bridges, transportation systems, and the safety of users. Scour around piers overlaps with several processes occurring at di fferent spatial and temporal scales, such as bed degradation and aggradation, dynamic braiding or meandering, and the formation/destruction of antidunes, large woody debris [69], barbs [107–109], or spur dikes for preserving the desired water depth [110]. Moreover, extreme flood events produce rapid changes of the local riverbed morphology, a ffecting the scouring process at bridge foundations. The temporal dynamics of scour, then, are intimately linked with sediment transport. This paper focused on the knowledge, gaps, and open questions related to local scour at bridge foundations in supercritical flows. From our review, the controlling mechanisms of scour in supercritical flows di ffer from those controlling scour in subcritical flows, due to the appearance of a detached hydraulic jump or vertical wall-jet patterns [20]. Interactions with the horseshoe and wake vortex systems (and also with the sediment motion) remain nearly unexplored (except for the work in [21]). The unexpected scour depth in the available experiments [6,27] suggests that the maximum scour depth in supercritical flows might be of comparable magnitude to that occurring in subcritical flows, even though the flow intensity is much higher. Further research is needed to understand the controlling parameters of the scour in supercritical flows.

#### *5.1. Measuring Techniques for Flow in the Laboratory*

Laboratory scour experiments with supercritical flows should avoid intrusive measuring techniques due to their important e ffect on the flow field (especially creating surface waves). E fforts should be made to transfer some widely used optical techniques from fluid mechanics to the hydraulics of supercritical flows, such as high speed image based velocimetry, including two dimensional and stereo PIV/PTV, or even the use of tomographic velocimetry, taking advantage of techniques like index matching to access the flow field in the scour hole.

#### *5.2. Measuring Techniques for Scour in the Laboratory*

Scour hole geometry might be best measured with precision ultrasonic or optic distance sensors. However, important constraints appear for intrusive instruments, such as sonars, especially at the laboratory scale because the size of the instrument can alter the flow field and create surface waves. Thus, the use of video cameras placed inside transparent bridge elements is recommended to record the maximum scour depth at the front of the bridge foundation over time.

#### *5.3. Measuring Techniques for Flow in the Field*

Field measurements of the supercritical flow at bridges might provide a good idea of the flow velocity upstream of the impacted foundations. Accessibility is, by far, identified as the main constraint in the use of intrusive equipment, so radar velocimeters [70] and video analysis, such as LSPIV [71], are recommended. As these methods provide only the surface velocity, further research is needed to correlate this data with the corresponding flow field and features.

#### *5.4. Measuring Techniques for Scour in the Field*

A major issue for river engineers dealing with bridge foundation design is to evaluate all the processes that could a ffect erosion for a better assessment of the scouring intensity and, consequently, a better optimization of the bridge foundation cost. Three main processes a ffecting the bed level generally include (i) the overall long-term bed evolution linked to the river equilibrium (indeed, many rivers in the world su ffers from erosion due to gravel mining or damming [111]); (ii) the natural river breath during a flood, leading to global erosion during the rising part of the flood and global deposition during the ebb part of the flood; and (iii) local erosion at the bridge foundation. Eventually, long term evolution should be tackled by being able to estimate the maximum erosion during an event but also to estimate the refilling of the scour after this event. Monitoring of very dynamic rivers remains quite di fficult but obviously needs some investment to be able to verify the upscaling limits from laboratory experiments. The measurement of the local scour depth at real bridges in supercritical flows or during floods has succeeded until now by only using the numbered brick method [5,75]. Further research is needed to develop methods using the structural behavior of the bridge for scour measurement. These kinds of indirect methods would allow for scour monitoring in complex hydro-sedimentary conditions.

#### *5.5. Physical Modeling of Scour in Supercritical Flows*

Given the constraints of knowledge transfer from sub to supercritical scour, and the important di fficulties for laboratory and field measurements of flow and scour at bridge foundations, the use of physical scale models appears to be a reasonable alternative for the analysis and design of particular cases. Important requirements include a wide set-up to prevent lateral confinement e ffects, high water and sediment discharges, and innovative measuring techniques in line with the involved rapid velocities. Moreover, important scale e ffects are expected in the case of model sediments with mean diameters smaller than 0.2 mm.

#### *5.6. Numerical Modeling of Scour in Supercritical Flows*

Classical coupled Navier-Stokes-Exner models have had some success in predicting the scour around bridge piles under subcritical flow conditions, even though some open questions remain to be answered. However, to the best of the authors' knowledge, no simulation of scour under supercritical flow conditions has ever been reported in the literature. Such simulations would be very challenging, particularly because of the very energetic flow conditions encountered in supercritical flows, the strong free surface dynamics, the multiple feedback mechanisms between the free surface dynamics, the flow hydrodynamics (e.g., HSV), and the sediment dynamics or the air entrainment. Some important breakthroughs can be expected in the near future by using multi-phase flow approaches in conjunction with high-resolution experimental data. From a numerical modeling standpoint, capturing the dynamics of a free surface is a critical prerequisite for numerical simulations of supercritical flows. To resolve the coupled flow field and interactions between the large-scale coherent structures of the HSV system and the free-surface, LES, or hybrid URANS–LES turbulence models should be tested to understand the flow physics and unsteady scour mechanisms. Eulerian–Lagrangian approaches seems unrealistic due to their very high computational cost. However, turbulence-resolving Eulerian–Eulerian simulations coupled with a free surface resolving capability will probably be possible in the near future.

**Author Contributions:** All eight authors (O.L., E.M., S.R., B.C., C.E., J.C., W.B. and S.M.) contributed to all aspects of present work in the framework of a one-week workshop at the University of Concepcion, Chile.

**Funding:** Financial support by the Chilean research council CONICYT through grants Fondecyt 1150997 and REDES 170021 is greatly acknowledged. C.E. acknowledges the support of Conicyt/Fondap gran<sup>t</sup> 15110017.

**Acknowledgments:** The authors would like to thank Nicolas Rivière (University of Lyon) for his scientific advice.

**Conflicts of Interest:** The authors declare no conflict of interest.
