Investigation of turbulent flows using spillway models aiming to aid downstream migration of fish

Dams and other flow control structures constitute obstacles to upstream and downstream aquatic habitats, reducing life‐cycle success and even eliminating diadromous and potamodromous fish species from river basins. Providing effective passage past hydroelectric dams is critical for restoring habitat connectivity and sustaining populations of fish species. Surface water release over spillways is effective in diverting fish from turbines and establishing a safe bypass for downstream migrants. Developing an effective passage system over spillways requires both biological knowledge of fish behavior and abilities, as well as hydraulic knowledge of spillway flows to provide hydrodynamic conditions that fish may exploit. The present study experimentally investigates several depths, velocity, and turbulence fields intended to promote the downstream migration of fish over spillways. Instantaneous velocity fields were measured in an open recirculating rectangular water channel. A 90° standard spillway model, as well as a spillway model with a modified upstream face slope of 45°, were tested for two water depths. The results show the presence of a distinct recirculation bubble at the heel of the 90° standard spillway with the shallower water depth. It was concluded that the upstream recirculation bubble may be suppressed by either increasing the water depth or decreasing the upstream face slope. Decreasing the upstream face slope also resulted in a more uniform distribution of acceleration and lower turbulence along the upstream face of the spillway. The modified spillways provide more suitable hydrodynamic conditions for downstream migrants.

This is because research on fish passage facilities began first with developing fishways to re-establish the free movement of upstream migrants and downstream migration problems, while understood as important by fisheries agencies, was acknowledged subsequently and addressed more recently . Furthermore, downstream passage measures are mostly designed for salmonids and often fail to provide the needed protection for other fish species Larinier & Travade, 2002). Although research targeting salmonid and non-salmonid species has increased (Li et al., 2021;Williams et al., 2012), considerable efforts are needed to fill the knowledge gap on fish responses to accelerating turbulent flows. For example, Li et al. (2021) reviewed previous research on fish responses to accelerating flows like those that occur over spillways.
These studies included juvenile Atlantic (Salmo salar) and Chinook salmon (Oncorhynchus tshawytscha), American shad (Alosa sapidissima), European eel (Anguilla anguilla), and Iberian barbel (Luciobarbus bocagei), while Li et al. (2021) reported on a juvenile cyprinid (Schizopygopsis younghusbandi). Improved understanding of accelerating turbulent flows over spillways and conventional fish passage facilities is essential to minimize the adverse effects of these barriers on river ecosystems, in which rare and indigenous species may be present.
Direct passage through hydro-turbines subjects fishes to various forms of stress or injury (barotrauma), such as impacts from turbine blades, abrupt variations in pressure, or cavitation, causing relatively high mortalities (Brown et al., 2014;Čada, 2001). Typical mortality rates for salmonids (juvenile salmon and trout) and American shad, vary from 5% to 90% in Francis turbines (Larinier & Travade, 2002).
Adult eels are especially vulnerable to passage through turbines due to their elongated bodies (Montén, 1985) and their thigmotactic behavior, which results in close contact with hydraulic structures (DWA, 2005;Richkus & Dixon, 2002). Out-migrating adult American eel (Anguilla rostrata) encounters two consecutive large hydroelectric dams on the St. Lawrence River. Turbine mortality rates of 26.4% were observed in Moses-Saunders, the first generating station eels go through, and 17.8% in Beauharnois, the next downstream one (Verreault & Dumont, 2003). Typical mortality rates for eels range between 15% to 30% in large hydro-turbines and even 50% to 100% in the smaller turbines used in small-scale hydroelectric dams (Hadderingh & Bakker, 1998;Larinier & Dartiguelongue, 1989;Montén, 1985). It is often not feasible to stop the operation of hydroturbines during downstream migration periods due to the unpredictable or lengthy characteristics of this activity, leading to power capacity shortage. Therefore, diverting and guiding fish away from turbine intakes is apparently the most pragmatic approach to pursue.
Most of the existing downstream fish passage facilities fall under one of the following categories: behavioral devices, screening systems, spillways, and bypass channels. Behavioral devices exploit the natural response of fish to certain triggers, such as visual, auditory, hydrodynamic, or electrical stimuli, to alter the migratory pathways of fish. Behavioral devices are convenient for power companies since they can be afforded at low enough costs, require minimum protection against clogging, and need minimal maintenance. However, the efficiency of behavioral devices depends on the configuration of the site and varies significantly with species. Furthermore, the repeated stimulation of fish may lead to a reduction in response and fish habituation (Coutant, 2001;Coutant & Whitney, 2000). Screening systems, on the other hand, are physical barriers that use meshes with small openings to prevent fish from passing through turbine intakes. Fish screens come in various forms, including wire mesh, wedge wire, perforated plate, ogee weir-shaped, or bar racks with various modifications (Amaral, 2003;Calles et al., 2013;. In recent years, screening systems have become affordable for small dams and irrigation canals.
For large-scale dams, due to large filtration areas and water intake footprints leading to relatively high development costs, as well as maintenance and cleaning problems, spillways and bypass channels are usually favored over screens .
Spillways are hydraulic structures that allow the release of surplus water into the downstream riverbed when the reservoir is full or when hydro-turbines reach their maximum capacity. In flow diversion applications, spillways are used to redirect the flow to a bypass channel.
Spillways may be categorized as service and emergency-type spillways based on the frequency of operation. A service spillway is a primary structure capable of handling discharge under design conditions. Emergency spillways are used in the unlikely event that flow discharge exceeds the design capacity of the service spillway (Ontario Ministry of Natural Resources, 2011). There are different types of service spillways, such as overflow, vertical drop, or chute spillways, depending on the site specifics. Spillways are also classified into uncontrolled and controlled spillways according to whether overflow is uncontrolled or regulated by gates (Jansen, 2003).
Previous studies have shown that surface water release over spillways, albeit with loss of some potential energy, is very effective in keeping the downstream fish migrants away from hydro-turbines and decreasing the forebay residence time (Arnekleiv et al., 2007;Ferguson et al., 2005;Johnson & Dauble, 2006). Furthermore, studies carried out across the United States, Canada, and Europe indicate that direct mortality as a result of passage through spillways is often relatively low (Larinier & Travade, 2002;Schwevers & Adam, 2020). Previous investigations have also revealed that the hydraulic environment induced by spillways is strongly dependent on the discharge rate and the specific geometry of the spillway (Savage & Johnson, 2001;United States Bureau of Reclamation, 1987). Consequently, various water depths over the crest or modifications to the upstream face slope that affect velocity distribution and flow acceleration near spillways, may test the swimming ability, and trigger behavioral fish responses which affect passage rates (Arnekleiv et al., 2007;Haro et al., 1998;Silva et al., 2015). Rates of passage success may also vary since swimming performance differs between groups of species and fish length (Katopodis & Gervais, 2016). Silva et al. (2015) performed live fish experiments in the laboratory to study the downstream movement behavior of the European eel and Iberian barbel over spillways with three different upstream face slopes of 90 , 45 , and 30 . The spillways were also tested for two water depths, 0.32 m and 0.42 m. For the European eel, successful passage rates per approach at the water depth of 0.42 m were 75%, 95%, and 92% for the 90 , 45 , and 30 spillways, respectively.
The corresponding values for the Iberian barbel were appreciably lower at 36%, 33%, and 37%. This study shows that although there are species-related differences, spillways with modified upstream face slopes are an improvement over the 90 standard spillway. At the water depth of 0.32 m, only 58% of European eels and 21% of Iberian barbels passed over the 90 standard spillway, which implies that increasing the water depth over the spillway may improve the passage efficiency. Silva et al. (2015) also performed acoustic Doppler velocimetry (ADV) and particle image velocimetry (PIV) to obtain point-wise and whole-field measurements upstream of the spillways, respectively. The ADV measurements were conducted upstream of the stan- Recent studies suggest that fish behaviors and migratory routes are affected by several hydraulic variables, such as turbulent kinetic energy (TKE), vorticity, and acceleration, that should be considered jointly for designing effective passage systems (Cote & Webb, 2015;Williams et al., 2012). Hence, measurements of flow characteristics are critical for improving spillway design and efficiency for the downstream migration of diverse fish species. The present study employs PIV to discuss the effect of the upstream face slope and water depth over the crest on not only the induced velocity field considered by Silva et al. (2015) but also acceleration and TKE to find the most suitable hydrodynamic conditions for the downstream migration of fish. T A B L E 1 Summary of the test parameters.  The water depth over the crest at the steady-state condition depends on the initial water depth in the flume, the net flow rate produced by the pump, and the upstream face slope of the spillway. The water depth over the crest was adjusted to the desired values by keeping the approach velocity constant while monitoring the water level and draining the surplus water from the channel. Two water depths over the crest, including D c ¼ 0:7h and 0:2 h, were tested for each spillway design to obtain four test cases. The room temperature was regulated at 20 ∘ C, and hence, the kinematic viscosity of water used as the working fluid was ν ¼ 1:0 Â 10 À6 m 2 =s.

| PIV system and measurement procedure
The instantaneous velocity fields were measured at the mid-span of the test section using a planar PIV system. A schematic showing several components of the PIV system is provided in Figure 3.
The flow was seeded with 10 μm silver-coated hollow glass spheres of specific gravity 1.4. In operating the PIV, it is important to examine the ability of the particles to faithfully follow the fluid motions since the velocities are calculated from the motion of the seeding particles. The slip velocity, u s , which is the difference between the local velocities of the fluid and seeding particle is estimated using the following expression: In Equation (1)

| RESULTS
Data analysis and post-processing were accomplished using commercial software Matlab ® . For each test case, the mean stream-wise velocity, U, and the mean vertical velocity, V, were obtained by averaging 12,000 instantaneous velocity fields. A summary of the obtained test parameters and pertinent dimensionless numbers is provided in  (Finnemore & Franzini, 2002). For all test cases, the upstream Froude number is less than one, whereas the Froude number over the crest of the spillway is greater than one, indicating sub-critical and supercritical flow, respectively. The mean stream-wise acceleration was determined by evaluating ∂U=∂x. The TKE was approximated using the following relation: where u 0 u 0 and v 0 v 0 are the stream-wise and vertical Reynolds normal stresses, respectively. In Equation (2), it is assumed that the span-wise Reynolds normal stress, w 0 w 0 , which was not directly measured, is

| Mean stream-wise velocity
Contours of the normalized mean stream-wise velocity, U=U o , are shown in Figure 5. As the flow approaches the spillway, the mean stream-wise velocity increases due to the reduction in cross-sectional F I G U R E 5 Contour plots of the normalized mean stream-wise velocity: [Color figure can be viewed at wileyonlinelibrary.com] area, eventually peaking above the crest. As evident from Figure 5, as the water depth decreases, the magnitudes of the normalized mean stream-wise velocities over the spillway increase. Decreasing the upstream face slope causes the trajectory of the streamlines near the crest to decrease, resulting in increased mean stream-wise velocity, which should be considered for designing safe spillway bypasses.
Overall, the flow discharges needed for optimizing the approach velocities to a spillway vary between species and affect the performance of the spillway in diverting fish species from turbines.
Negative regions of mean stream-wise velocity are observed near the heel of the 90 ∘ standard spillway. Hence, it can be concluded that the oncoming flow separates from the channel floor, which is attributed to the adverse pressure gradient induced by the spillway. The onset of the separation may be estimated using the isopleth of

| Mean vertical velocity
Contours of the normalized mean vertical velocity, V=U o , are presented in Figure 6. For all test cases, regions of highly positive mean vertical velocity are observed around the crest due to the upward deflection of the flow by the upstream face of the spillway. Over the spillway, the flow is accelerated by gravity, causing the mean vertical velocity to increase in the flow direction. As observed from Figure  The behavioral responses of fish to accelerating flows depend on species, stage of development, schooling behavior, and fish size (Li et al., 2021;Silva et al., 2015;Williams et al., 2012). Swimming speeds increase with the square root of the fish length (Katopodis & Gervais, 2016); hence, larger species can negotiate higher water velocities and accelerations. Since downstream migration often involves juveniles, correct predictions of the mean stream-wise acceleration are essential for increasing passage efficiency. It is known that uniformly accelerating flows are more suitable for passage entrance designs. Rheophilic species, including salmonids and cyprinids, avoid rapidly accelerating flows even when encountering facilities at dams that are designed to guide them away from turbines due to evolved behavioral responses . Haro et al. (1998) found that uniform water acceleration at surface bypasses increased the downstream passage rate of both Atlantic salmon and American shad and promoted school integrity. Li et al. (2021) also reported higher downstream passage rates for Schizopygopsis younghusbandi under low acceleration conditions. Silva et al. (2015) reported higher success rates for the downstream passage of Iberian barbel through modified spillways, which was again attributed to the uniformity of flow acceleration. Figure 7 shows that for the 90 ∘ standard spillway, the contour levels are concentrated around the crest, whereas for the 45 ∘ Downstream migrant species may vary their responses to turbulent and accelerating flows. Depending on species, state of physiological development, fish size, and schooling behavior, such responses may include holding position before moving downstream, actively migrating, switching rheotaxis, exhibiting avoidance behaviors, or even escaping upstream (Li et al., 2021;Silva et al., 2015;Williams et al., 2012). Evidence shows that several fish species, including Schizopygopsis younghusbandi, European eel, Iberian barbel, Atlantic salmon, and rainbow trout (Oncorhynchus mykiss), tend to occupy areas with low turbulence levels to minimize the energy expenditure required for maintaining their position (Li et al., 2021;Santos et al., 2012;Shahabi et al., 2021). Hence, the 45 ∘ modified spillway may increase the downstream passage efficiency compared to the 90 ∘ standard spillway due to relatively lower TKE values along the upstream face of the spillway.

| One-dimensional profiles
One-dimensional profiles of the mean velocities and TKE are presented in Figure 9. Although contour plots allow for whole-field comparison of several test cases, they cannot provide the needed quantitative accuracy for estimation of flow characteristics upstream of the spillway, especially since the values over the spillway are generally orders of magnitude larger than those measured upstream. Onedimensional profiles are better suited for providing detailed measurements of flow characteristics upstream of the spillway. The profiles may directly be compared to the obtained results from computational fluid dynamics (CFD) for validation of numerical models or to upscale the measurements for a spillway prototype using Froude number similarity.
The practicality of constructing spillway prototypes with a non-vertical upstream face leads to additional considerations. The profiles at four successive stream-wise locations, x=h ¼ À1:5, À 1:0, À 0:5, and À0:2, were staggered relative to one another to better visualize the stream-wise evolution of the flow F I G U R E 9 Streamwise evolution of the normalized mean velocities and turbulent kinetic energy profiles for different upstream face slopes at D c =h ¼ 0:7 (left) and D c =h ¼ 0:2 (right). [Color figure can be viewed at wileyonlinelibrary.com] characteristics. The profiles for different upstream face slopes were then superimposed on top of each other to show the effects of the upstream face slope. For each test case, the range of the vertical axis is limited to 1 þ D c =h. Moreover, since the upstream face of the 45 ∘ modified spillway stretches from x=h ¼ 0 to À1, in this region, the profiles start at y=h ¼ 1 þ x=h.
From Figures 9a,b, it can be seen that at x=h ¼ À1:5, the profiles almost collapse on top of one another. The profiles diverge as the flow evolves in the stream-wise direction, and the mean stream-wise velocity increases as the upstream face slope decreases. This is due to the fact that the flow cross-sectional area is smaller along the upstream face of the 45 ∘ modified spillway compared to the 90 ∘ standard spillway. Furthermore, comparing Figure 9a,b, it is apparent that the effect of decreasing the upstream face slope is more evident at lower water depths.
From Figures 9c,d, it is evident that at x=h ¼ À1:5, the mean vertical velocity is almost zero for all test cases. The profiles diverge as the flow evolves in the stream-wise direction, and the mean vertical velocity increases due to the upward deflection of the flow caused by the upstream face of the spillway. Comparing Figures 9c,d, it can be seen that the effect of decreasing the upstream face slope is more apparent at lower water depths. Although the mean vertical velocity increases as the upstream face slope decreases, this is not a general conclusion as was observed in Figure 6.
From Figures 9e,f, it can be seen that at x=h ¼ À1:5, the TKE is almost zero for all test cases. As the profiles evolve in the stream-wise direction, the magnitude of the TKE increases significantly for the 90 ∘ standard spillway. For the 45 ∘ modified spillway, on the other hand, highest levels of turbulence are observed at the heel of the spillway, x=h ¼ À1:0, and the magnitude of the TKE gradually decreases in the stream-wise direction. For the 45 ∘ modified spillway, the profiles affect a small range and are almost zero everywhere except in the vicinity of the walls. Meanwhile, for the 90 ∘ standard spillway, the profiles cover a relatively wider range.