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. 2026 Feb 19;108(6):2010–2028. doi: 10.1111/jfb.70368

Modelling experiments reveal fish swimming strategies in the vertical slot fishway: Insights from swimming behaviours, kinematics and trajectory energy benefits

Xiaoming Yan 1, Fei Liu 2, Chenyang Cao 1, Shikang Liu 1, Qihao Meng 1, Yuqian Xi 1, Lijian Ouyang 1,3, Weiwei Yao 1,✉
PMCID: PMC13357342  PMID: 41713866

Abstract

The vertical slot fishway (VSF) has been widely installed to help fish pass hydropower dams, mitigating migration barriers from dam construction. Current research on VSF construction has not fully incorporated the fundamental principles of fish swimming kinematics and the quantification of trajectory characteristics, which is of great significance for optimizing existing VSFs and guiding future development. This study investigated the swimming behaviours, kinematics and trajectory characteristics of Procypris rabaudi (P.R.), Onychostoma sima (O.S.) and Squalidus argentatus (S.A.) in a VSF. Kinematics metrics included tail‐beat frequency, angle, amplitude, midline kinematics and wavelength. The results demonstrated that the passage rate for the three fish species (8–10 cm body length) decreased as the outlet velocity increased. Analysis of trajectory hydraulic complexity revealed that swimming along side walls and baffles provided greater energy benefits. Furthermore, fish exhibited the lowest tail‐beat frequency in recirculation zones, whereas the midline oscillation amplitude and wavelength progressively decreased from recirculation zones to the mainstream and slots. Long‐term retention behaviours were also observed to adversely affect passage efficiency. This study thereby enhances understanding of fish swimming strategies and trajectory characteristics in VSFs.

Keywords: fish behaviour, hydrodynamics, swimming kinematics, trajectory, vertical slot fishway

1. INTRODUCTION

The development of water conservancy projects is beneficial for water storage, irrigation, flood control and navigation (Chen et al., 2015; Hossain et al., 2010; Kuriqi et al., 2019). High dams and hydropower stations have been heavily constructed in mountain rivers all over the world (Botelho et al., 2017; Kuriqi et al., 2021). Habitat fragmentation and disrupted river connectivity as a result of the construction of these hydraulic complexes are regarded as vital ecological problems to the conservation of aquatic biodiversity (Benejam et al., 2016; Carolli et al., 2023; Liermann et al., 2012; Zarfl et al., 2019), including the survival of freshwater fish. The migration routes of fish in original rivers are blocked due to the presence of large dams (Poulet, 2007), and thus there is a lack of genetic exchange in fish upstream and downstream of the dams (Duponchelle et al., 2021), which may affect the biodiversity of fish populations (Kolden et al., 2016; Yagci, 2010). For instance, great mortality of the European eel occurred when they passed through turbines during their migration to spawning grounds (Pedersen et al., 2012). The construction of dams and other hydraulic structures for energy production continues to alter river ecosystems, adversely affecting the survival and reproduction of aquatic life. To address this issue, there is a critical need to implement measures that reconnect upstream and downstream habitats, facilitating the free movement and genetic exchange of aquatic species, thereby mitigating the conflict between ecological conservation and economic development.

Fishway, defined as a passage that assists fish to cross dams and any obstacles, has been designed to mitigate the ecological pressure on fish caused by dam construction (Branco et al., 2013; Clay, 1995; Romao et al., 2019; Santos et al., 2012; Silva et al., 2018). Vertical slot fishways (VSFs) are universally adopted as a compensation method for fish migration passage in hydraulic engineering (Valbuena‐Castro et al., 2020). This is attributed to their great compatibility with a wide range of fish species (Katopodis & Williams, 2012; Rajaratnam et al., 1986). Considerable research has been carried out to facilitate the construction and optimization of VSF. Up to now, these studies mainly focused on three aspects: (1) The investigation and improvement of hydrodynamic characteristics of vertical slots, mainstream and recirculation zones for different types of VSF (Fuentes‐Pérez et al., 2018; Marriner et al., 2016; Puertas et al., 2012; Rajaratnam et al., 1992). (2) Swimming ability of various fish species for designing the velocities in the pools, inlets and outlets (Cao et al., 2017; Katopodis et al., 2019; Quaranta et al., 2019; Shi, Ke, et al., 2022b). (3) Laboratory and case experiments about captured species, passage rate and time based on trajectory distribution (referring to the spatial patterns and frequency of paths taken by fish through the fishway) (Bao et al., 2019; Li et al., 2021; Noonan et al., 2012; Shi et al., 2024). These fundamental theories reached a consensus that the efficiency of VSF was extremely low. Researchers have also conducted the above research for 93 existing fishways in China (data as of August 2020). The engineering scale of fishways in China was greater due to the high grade of Chinese dam engineering in general, such as the over 3‐km fishway at the ZM Hydropower Station, which further aggravated the challenge of fish migration and population conservation (Shan et al., 2022). Enhancing VSF efficiency and optimizing VSF designing still possess an enormous scientific research value worldwide.

Fish swimming kinematics based on tail‐beat kinematics was developed to evaluate and quantify fish behaviours influenced by different environmental conditions (Batty & Domenci, 2021; Di Santo et al., 2021). Intense flow velocity brings a high locomotive cost for fish with a high tail‐beat frequency (van Weerden et al., 2014). Admittedly, fish tail‐beat amplitude was strongly associated with the fishway width. However, swimming kinematics on how fish respond to various hydrodynamic conditions corresponding to different fishway positions still remains partially understood in the field of fishway construction. The optimization and designing of fishway size, shape and types should consider the fish swimming kinematics in different positions (e.g., tail‐beat movement in slots and recirculation zones). Furthermore, existing studies have also examined various fish trajectory profiles and swimming preference in fishways (Li et al., 2021). For instance, some fish exhibit a preference for swimming along the walls to minimize energy expenditure, whereas others may utilize specific flow refuges. The trajectory characteristics was strongly associated with the designing of fishway pools (Zheng et al., 2022). Basically, longer side walls and baffles generated wider recirculation area and longer trajectory (Wang et al., 2010). It is unknown that why fish selected one trajectory as their preference route and how significant are the differences among each trajectory. The simple categorization of trajectories into mainstream and recirculation trajectories was unable to satisfy designing principles of fishway pools and our understanding of fish trajectory characteristics in the VSF. A critical limitation lies in the lack of a combined analysis that links the energy benefits of specific trajectories with a detailed swimming ethology. The energetic rationale behind path selection and the behavioural sequences in complex flows are thus poorly understood, which our study aims to resolve. Therefore, further research on fish behaviours and trajectory characteristics in the designing and optimization of VSF should be conducted.

Through optimization research on the fishway of the Changzhou Water Control Project, the results indicate that the arrangement of a Different Side Vertical Slot Fishway can create uniform recirculation zones and stable main flow zones, better meeting the requirements for energy dissipation and fish passage (Rui et al., 2022). This type of Different Side Vertical Slot Fishway is one of the main types of fishways in China. Therefore, this study selects the Different Side Vertical Slot Fishway as the subject of research. Many experiments used a single pool as the research object to investigate hydrodynamics and fish trajectory distribution in VSF (Shi et al., 2024; Wang et al., 2010); these studies considered that the hydrodynamics of all pools were equal. In actual dams, the hydrodynamics of the outlet pool (the final pool adjacent to the reservoir forebay) in a VSF differ from those of ordinary pools due to forebay pressure (Silva et al., 2018). Consequently, the flow velocities in all upstream pools are determined by the conditions introduced at this outlet pool. Therefore, investigating fish swimming kinematics and trajectory distribution in two continuous pools, where one is the outlet pool, can further our understanding of trajectory continuity and guide the velocity design of VSF outlet pools.

Accordingly, this study aims at further investigating the swimming kinematics and trajectory characteristics of Procypris rabaudi (P.R.), Onychostoma sima (O.S.) and Squalidus argentatus (S.A.) in a Different Side Vertical Slot Fishway. Firstly, we simulated the fishway hydrodynamic characteristics with module calibration. Then, we mapped out different trajectory types based on swimming preference in two pools and calculated the passage rate and proportion of each trajectory. This study was guided by the following hypotheses: (1) distinct fish trajectories within the VSF are formed as behavioural responses to specific local hydrodynamic conditions, and these trajectories differ significantly in their associated energy costs for fish; (2) fish swimming kinematics exhibit predictable variations across different flow zones (uniform flow, slots, mainstream, recirculation), reflecting their strategy for energy conservation and passage negotiation. To test these hypotheses, we quantified the hydrodynamic characteristics of each trajectory and conducted a combined analysis of trajectories and hydrodynamics to elucidate the mechanism of trajectory formation. Moreover, we investigated fish swimming kinematics under uniform flow, vertical slots, mainstream, and recirculation zones to further quantify fish behaviours in the VSF. The final results provide a valuable reference for optimizing fishway design and evaluating fishway efficiency from the perspective of fish swimming kinematics and trajectory distribution.

2. MATERIALS AND METHODS

2.1. Experimental fish

Fishery resources in the upper reaches of the Yangtze River are extremely abundant, particularly in the mountainous basins of Southwest China where hydropower stations are widely distributed (Liu et al., 2024). This study was conducted in the Chishui River basin (central co‐ordinates: approximately 27.8° N, 106.3° E) within the upper Yangtze region, an area characterized by complex ecosystems and rich aquatic biodiversity, especially in fish species (Cao et al., 2025; Xi et al., 2025). Among them, P.R., O.S. and S.A. are identified as rare fish species in the upper Yangtze (see Figure S1 in the supplementary materials). P.R. is listed as a national second‐class protected animal in China, O.S. serves as an important local economic species and S.A. is included in the IUCN Red List of threatened species (Ouyang et al., 2025). These species were selected as representative target species for fishway passage in the upper Yangtze, exhibiting distinct passage strategies due to their differing ecotypes and swimming capabilities. This diversity allows our study to assess the VSF's performance across a biologically relevant range of passage challenges. Basic information on the experimental fish is provided in Table 1.

TABLE 1.

Physical parameters of target fish species.

Fish species Length (L, cm) Weight (W, g) Height (H, cm) H/L Habitat characteristics Preference for water flow
Procypris rabaudi 10.7 ± 0.6 19.8 ± 1.1 3.5 ± 0.2 0.33 It lives in deep‐water environments with rocky or gravelly substrates at the bottom. Prefers rapids
Onychostoma sima 13.3 ± 0.8 22.6 ± 1.6 3.2 ± 0.4 0.24 It inhabits the bottom layer of water bodies and is commonly found in shallow areas and rocky stretches of clear streams and rivers. Prefers rapids
Squalidus argentatus 9.3 ± 1.1 10.3 ± 2.4 1.3 ± 0.2 0.14 It moves about in the bottom layer of water bodies, preferring to live in areas with slow‐flowing water, such as river bends, canals and backwaters of rivers. Prefers slow‐moving
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The experimental fish – P.R., O.S. and S.A. – were obtained through field capture using seine nets during the low‐flow season (October–November 2023). After capture, they were immediately transferred to oxygenated transport tanks and conveyed to the experimental site within 2 h. In the laboratory, fish were kept by species in three circular oxygenation acclimation tanks, each with a radius of 1 m. Water temperature was maintained at 18°C–20°C, pH at 7.1 and dissolved oxygen concentration at 7.0–10.0 mg/L during the 3‐day acclimation period. The fish were fed a specialized commercial pellet diet twice daily at 9:00 AM and 20:00 PM, and feeding was suspended 48 h prior to formal experiments.

2.2. Experimental set‐up and protocol

The diagram of the experimental VSF is presented in Figure 1a,b. The VSF model was a separated device, which was equipped in the swimming chamber of the Fish Swimming Flume System (Figure 1b). The Fish Swimming Flume System is a water flow self‐circulation system to generate circulating current in the VSF. A honeycomb screen was placed in the upstream to stabilize the flow and generate the uniform flow, and a tailgate grid was fixed in downstream to prevent fish from propeller entrainment. There were two pools in VSF model: pool‐1 represented the ordinary pool, and pool‐2 represented the outlet pool (the last pool in realistic fishway engineering) in the VSF. This study defined the velocity into pool‐2 as the outlet velocity of the VSF, which was directly determined by the propeller controlled by the motor. Three slots were labelled in Figure 1b. The pool size is presented in Figure 1c and Table 2. Fish swimming behaviour and trajectory routes were recorded using a high‐definition camera (MV‐SUA133GC, MindVision Technology Co. LTD) installed above the test area (Figure 1d).

FIGURE 1.

FIGURE 1

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Schematic of the experimental set‐up: (a) diagram of a Different Side Vertical Slot Fishway, (b) the experimental fishway model installed in the Fish Swimming Flume System (Model: FBT‐90 L, Qingdao Starfish Co., Ltd.), (c) dimensions of pool‐1 within the experimental fishway and (d) top and side views of the fishway captured from the experimental video.

TABLE 2.

Specifics of structural parameters of a single pool.

Length of pool (L) Width of pool (B) Width of baffles (d) Width of slots (b) Length of baffles (l 1 ) Length of baffles (l 2 ) Water depth Deflecting angle of slot (θ)
22 cm 20 cm 1 cm 6 cm 5 cm 9 cm 20 cm 45°
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The experimental set‐up maintained consistent water temperature, pH and dissolved oxygen levels with the acclimation tanks. All three species exhibit crepuscular and nocturnal activity patterns and are most active during dusk and night‐time hours. In consideration of this behavioural characteristic, experiments were scheduled between 18:00 PM and 22:00 PM to align with their peak activity period. For each trial, fish were randomly selected and allowed to acclimate to the flow conditions for 30 min, followed by a test duration not exceeding 20 min. Each individual fish was used only once in the fishway experiment. After testing, fish were temporarily held in separate, identifiable tanks before being released back into their original capture river.

Figure 2 illustrates the experimental procedure and methodological workflow used to investigate fish swimming strategies in the VSF. Before the formal experiments, target fish was put into the adaptation area to accommodate the water flow. The adaptation velocity was 0.05 m/s, and a piece of gauze was placed at slot‐3 to guarantee adequate adaptation time (30 min) for test fish and avoid stress response during testing. After 30‐min adaptation time, the outlet velocity was accelerated to 0.1, 0.2, 0.3 and 0.4 m/s, respectively. The experimental velocities (0.1–0.4 m/s) were selected to represent the range of flow conditions in prototype VSFs, which are subject to varying operational water levels. This range was determined by applying Froude number similarity to our 1:10 scaled physical model, ensuring that the tested conditions encompass ecologically relevant field scenarios. The passage time for each pool was 5 min, and complete passage of fish from slot‐1 to slot‐3 was regarded as a successful passage. The passage rate and time for complete passage would be counted after all experiments ended. Each velocity treatment included 51 fish for each species, and each fish was tested only once. For the failed passage fish, their swimming process was still recorded for further analysis. The experimental videos would be inserted using Logger Pro software (version 3.12, Vernier Software & Technology) to obtain the swimming behaviour metrics.

FIGURE 2.

FIGURE 2

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Flowchart of the methodology for analysing the fish swimming behaviour in the fishway.

2.3. Quantification of trajectory characteristics

Fish trajectory routes were extracted from experimental videos by plotting their co‐ordinate positions using Logger Pro software. Typical trajectories for two pools would be presented for further analysis. Firstly, the trajectory characteristics were quantified by depicting the hydrodynamic parameters of each typical trajectory. Then, two habitat metrics, M 1 and M 2, were used to describe the impact of the hydraulic complexity of all trajectories on fish energy benefits (Crowder & Diplas, 2000; Gualtieri et al., 2017). M 1 (J/kg m) is the spatial gradient of kinetic energy per unit mass and per unit distance. M 1 is directly proportional to the drag force that an organism is subjected to and a measure of the energy expended to move from one place to another. M 2 (1/m) indicates the average rate of change in kinetic energy per unit mass and unit length between two locations, which is similar to M 1 but scaled by flow kinetic energy where the velocity is relatively lower. The two metrics can be calculated by following formulas:

M1=VavgV2−V1∆s (1)
M2=2VavgV2−V1/∆sVmin2 (2)

where V 2 and V 1 are the velocity values measured a distance ∆s apart, V avg is the average velocity between points 2 and 1 and V min is the minimum velocity of V 2 and V 1.

2.4. Swimming kinematics

Fish swimming kinematics were quantified by comparing their tail‐beat kinematics (tail‐beat frequency, angle and amplitude), midline kinematics and wavelength under mainstream, recirculation zones, vertical slots and uniform flow. Tail‐beat frequency is the times of a complete tail‐beat movement within 1 s, and a complete tail‐beat movement refers to the progress that fish's tail fin reaches its highest point and then goes back to the same highest point again. Tail‐beat angle is formed by two lines, one is the body rigid line segment (Akanyeti & Liao, 2013) and another is the body flexible line segment. Tail‐beat amplitude refers to the vertical distance from tail end to body rigid line segment. Wavelength is the swimming distance that fish completes an entire tail‐beat movement, which can be calculated by dividing the swimming speed by the tail‐beat frequency (Liu et al., 2024).

2.5. Numerical simulation

This study employs computational fluid dynamics (CFD) for a three‐dimensional numerical simulation of the flow structure (Li et al., 2019). The standard k‐ε turbulence model is used to solve the three‐dimensional Navier–Stokes equations (Stamou et al., 2018; Zheng et al., 2022). A hexahedral structured grid was applied to the computational domain with local refinement at the vertical slot. Grid independence was verified using three mesh schemes (M 1, M 2, M 3; Table S1). Velocity results from M 1 and M 2 agreed closely (difference <0.93%), whereas M 2 and M 3 showed a larger discrepancy (>10.2%). One‐way analysis of variance (ANOVA) (SPSS) confirmed no significant difference between M 1 and M 2 (p = 0.968). Therefore, the M 2 scheme (size: 0.005 m; slot size: 0.003 m) was selected for all simulations (Zheng et al., 2022). The inlet and outlet of the fishway were set as pressure boundary conditions, with the water surface at atmospheric pressure and no‐slip conditions assigned to the bottom and side walls (Yan et al., 2023).

To verify the accuracy of the mathematical model, 300 measurement points were selected in the experimental model for comparative analysis. After summarizing and analysing the flow velocity and turbulent kinetic energy at all measurement points, the flow velocity error ranged from 2.11% to 23.13%, with an average of 6.67%; the turbulent kinetic energy error ranged from 4.36% to 23.65%, with an average of 8.32% (Figure S2). Based on these results, the mathematical model is considered capable of accurately calculating the flow structure in the fishway.

2.6. Statistical analysis

One‐way ANOVA with post hoc multiple comparisons was used to calculate the significant difference among each variable for metrics used in this study, including hydrodynamic differences of each trajectory, M 2, M 1, three tail‐beat kinematics metrics and wavelength under mainstream, recirculation zones, slots and uniform flow. Dunnett's T3 test was employed when variance was nonhomogeneous. The threshold of a significant difference was set at a p‐value of 0.05.

3. RESULTS

3.1. Hydrodynamic status and swimming zones

Flow velocity, turbulent kinetic energy (TKE) and total hydraulic strain (TS) distribution of the ordinary pool (pool‐1) and the fishway outlet pool (pool‐2) under four hydrodynamic conditions in the fishway are presented in Figure 3. Notably, two pools that shared the symmetrical configuration exhibited different hydrodynamic characteristics; the profile of high‐velocity zone in pool‐1 was more curved. Higher outlet velocity generated higher hydrodynamic intensity in both pools, and the hydrodynamic intensity in the mainstream zone was stronger than that in the recirculation zones.

FIGURE 3.

FIGURE 3

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Distribution of flow velocity (a), turbulent kinetic energy (b), total hydraulic strain (c), velocity vector (d) and mainstream and recirculation zones (e) for two pools under different flow conditions (I, II, III and IV represent inlet velocities of 0.1, 0.2, 0.3 and 0.4 m/s, respectively).

The area of the high‐velocity zone increased with an increasing in outlet velocity, and the maximum velocity of mainstream reached 0.52 m/s under an outlet velocity of 0.4 m/s (Figure 3, a‐IV). The velocity range of recirculation zones was 0–0.16 m/s across four outlet velocities. The TKE value of mainstream in pool‐2 was lower than that in pool‐1. TKE values near slot‐2 and slot‐1 were much higher, and the TKE value near slot‐1 reached 0.018 m2/s2 under outlet velocity of 0.4 m/s. Compared to TKE intensity under outlet velocity of 0.1–0.2 m/s, the TKE intensity in recirculation zones was much stronger under 0.3–0.4 m/s. In Figure 3c, the TS value in the middle region of mainstream was lower than that on both sides, and TS value near three slots varied a lot and reached the maximum value (30 1/s). Similarly, the TS of recirculation zone‐4 was larger under outlet velocity of 0.4 m/s.

Based on the velocity vector for each outlet velocity condition, the schematic diagram of mainstream and recirculation zones is presented in Figure 3e, and their area proportions are shown in Table 3. Significantly, the increasing outlet velocity decreased the area proportion of all recirculation zones and expanded mainstream proportion. Recirculation zone‐4 occupied the smallest proportion among all recirculation zones.

TABLE 3.

Comparison of the area proportions of the recirculation and mainstream zones for four inlet velocities.

Inlet velocity (m/s) Area proportions (%)
R‐1 R‐2 R‐3 R‐4 Mainstream
0.1 17.62 21.08 25.71 12.43 23.16
0.2 16.14 21.71 24.86 12.28 25.01
0.3 14.71 20.57 24.14 11.28 29.3
0.4 13.86 19.71 23.57 9.42 33.44
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3.2. Combining fish swimming preference, trajectories and hydrodynamics

The passage rate and time of three species at two slots are presented in Table 4. Higher outlet velocity decreased the success rate of fish passing through fishway and increased the passage time of two slots across four outlet velocities for each species. The passage rates under outlet velocity of 0.1–0.2 m/s were relatively higher, for example 70.59% of S.A. successfully passed through the fishway under 0.1 m/s. Besides, the passage time of P.R. (13–30 s) was generally longer than that of the other two species (9–20 s). For O.S., their passage rate under outlet velocity of 0.2 m/s was significantly greater than that under other outlet velocities.

TABLE 4.

Comparison of the number of fish trials, passage rate and time of slot‐2, as well as success rate and passage time for passing through fishway under each flow velocity.

Fish species Inlet velocity (m/s) Trials Passage rate for slot‐2 (%) Passage time for slot‐2 (s) Passage rate (%) Passage time (s)
Procypris rabaudi 0.1 51 70.59 6.79 ± 1.43 47.06 13.65 ± 2.43
0.2 51 52.94 8.84 ± 1.15 23.53 20.36 ± 2.66
0.3 51 62.75 8.32 ± 1.33 52.94 19.64 ± 3.11
0.4 51 47.06 9.22 ± 1.04 13.73 30.78 ± 5.34
Onychostoma sima 0.1 51 47.06 2.07 ± 0.93 37.25 9.74 ± 1.83
0.2 51 76.47 3.20 ± 1.93 66.67 10.64 ± 3.22
0.3 51 56.86 5.10 ± 1.62 23.53 12.68 ± 2.16
0.4 51 43.14 6.17 ± 2.10 13.73 14.11 ± 5.33
Squalidus argentatus 0.1 51 80.39 4.09 ± 1.47 70.59 15.46 ± 4.12
0.2 51 70.59 5.87 ± 3.41 62.75 16.92 ± 5.23
0.3 51 62.75 8.27 ± 1.23 23.53 18.41 ± 4.77
0.4 51 37.25 10.54 ± 2.71 9.80 21.57 ± 5.86
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For all fish that successfully passed through two fishway pools, their swimming preference under four outlet velocities is shown in Figure 4. Obviously, fish were found to avoid the high‐velocity zone and be active in four recirculation zones with relatively lower velocity, especially the areas adjacent to the walls. Under outlet velocities of 0.1–0.3 m/s, fish had a wider activity range and crossed more frequently among four recirculation zones. Fish would like to swim in the recirculation zone‐2 and zone‐4 at 0.4 m/s. Besides, fish movement near three slots was more frequent compared to other mainstream and recirculation zones (occurrence number ≥ 40).

FIGURE 4.

FIGURE 4

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Swimming preference of three fish species under different outlet flow velocities (I, II, III and IV represent outlet velocities of 0.1, 0.2, 0.3 and 0.4 m/s, respectively): (a) Procypris rabaudi, (b) Onychostoma sima, (c) Squalidus argentatus.

By analysing the swimming preferences and trajectories of all successful passages, we identified six distinct passage routes (Figure 5a,b) and nine trajectory combinations with their proportional usage (Figure 5c). As the flow velocity increased, the diversity of trajectory types selected by fish decreased significantly. Notably, the Tc‐T₃ combination was the only trajectory observed across all tested flow conditions. Trajectories T1 and T3 in pool‐2, along with Ta and Tc in pool‐1, were classified as recirculation trajectories, whereas T2 (pool‐2) and Tb (pool‐1) represented mainstream trajectories. The two pools exhibited distinct trajectory profiles due to their different hydrodynamic characteristics (Figure 5a). Higher proportions of straight‐line segments near side walls were observed in Ta, Tc and T3, indicating a preference for wall‐following behaviour. Between the mainstream trajectories, T2 showed a more curved profile than Tb. The Tc‐T3 combination was the most frequently selected route across pools (Figure 5b). Notably, trajectories containing T2 or Tb were increasingly avoided at higher velocities, as these paths exposed fish to high‐flow zones in the fishway. Consequently, the Tc‐T3 combination became the dominant route through the slots with increasing outlet velocity (e.g., reaching 71.8% for P.R. at 0.3 m/s).

FIGURE 5.

FIGURE 5

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Six passage routes (a), the proportion of each trajectory (b) and the proportion of nine trajectory combinations for three species (c) under four inlet velocities.

To further analyse the distribution of hydraulic characteristics and energy benefits along the trajectories, the flow condition with an outlet velocity of 0.3 m/s was selected as a representative case for detailed discussion. This selection was made because the four tested flow conditions in this study exhibited similar flow structures and fundamentally consistent distribution patterns. The hydrodynamic characteristics of each trajectory under an outlet velocity of 0.3 m/s are presented in Figures 6a–c and S3. Trajectories Tb and T2 in the mainstream possessed the highest flow velocities; the velocities of the other four trajectories were relatively lower but exhibited a broader range of values as they covered both mainstream and recirculation zones. Notably, the TKE for Tc in recirculation zone‐4 (0.003 m2/s2; Figure 6b) was higher than that in other zones due to the presence of the high TKE at slot‐1. The TKE of T2 (0.0003 m2/s2) in mainstream was the lowest due to the minimal velocity fluctuations along T2. Consistently, the TS of each trajectory remained below 10 s−1 (Figure 6c), whereas the TS for T3 reached 50 s−1 because the end of T3 was adjacent to slot‐3.

FIGURE 6.

FIGURE 6

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Combined analysis of typical trajectories and hydrodynamic characteristics at 0.3 m/s outlet velocity. (a) Velocity distribution, (b) turbulent kinetic energy (TKE) and (c) total hydraulic strain (TS). Hydraulic complexity metrics: (d) M 1 , (e) M 2 and (f) velocity gradient. Lowercase letters indicate significant differences (p < 0.05) among trajectory routes.

The hydraulic complexity and fish energy expenditure of each trajectory quantified by M 1 and M 2 are depicted in Figure 6d–f, which present the velocity gradient specific to each trajectory. In general, the high value of the two metrics emerged where the TS varied a lot, such as at the intersection of the mainstream and recirculation zones. Both parameters exhibited a wide spatial range of kinetic energy change; however, their average values were relatively low, indicating the simple hydraulic variation in most areas of each trajectory. The range of M 1 for most areas along each trajectory was 0–0.5 J/kg m (Figure 6d), indicating that the drag force experienced by the fish was similar for each trajectory. However, the M 2 of trajectory Tb (7.61 1/m) and T2 (3.12 1/m) had low values due to the narrow range and low variability in their velocity gradients (Figure 6f), whereas this metric for the remaining four trajectories in recirculation zones was particularly large (0.25–98.55 1/m). Compared to trajectory Tb and T2 specific to mainstream zones, fish that swam with trajectories in recirculation zones obtained more energy, where the velocity gradients were much stronger, for example, fish swimming along Tc obtained the greatest kinetic energy (M 2 = 37.51 1/m, Figure 6, d2).

3.3. Tail‐beat kinematics and fish morphology in fishways

The tail‐beat frequency, amplitude and angle of three species in different scenarios (recirculation zones, mainstream zones, vertical slots and uniform flow) and under four outlet velocities are shown in Figure 7 and Table S3. Obviously, the higher tail‐beat frequency and lower amplitude and angle examined that the tail‐beat movement of three species was more intense under uniform flow.

FIGURE 7.

FIGURE 7

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Tail‐beat frequency, amplitude and angle of Procypris rabaudi (a), Onychostoma sima (b) and Squalidus argentatus (c). Lowercase letters indicate significant differences (p < 0.05) in tail‐beat kinematics among different positions under the same inlet flow velocity, whereas capital letters indicate significant differences among different inlet velocities at the same position.

Generally, fish tail‐beat frequency at each position increased with an increasing in outlet velocity. According to the ANOVA results, the tail‐beat frequency of P.R. and S.A. in the mainstream zones and vertical slot was larger than that in recirculation (Figure 7, a1 and c1). But the tail‐beat frequency of O.S. in mainstream zones was particularly higher than that in other two positions (Figure 7, b1); no significant difference existed between mainstream and uniform flow under 0.1 m/s. Fish tail‐beat amplitude generally exhibited decreasing trend with the increasing outlet velocity. The relationship of tail‐beat amplitude for P.R. and S.A. at different positions was recirculation zones>mainstream zones>vertical slots, whereas that of O.S. in mainstream zones was the lowest compared to other two positions (Figure 7, a2, b2 and c2). The tail‐beat angle in recirculation zones was significantly higher than that in other two positions. The angle difference of each species between mainstream zones and vertical slots was tiny under outlet velocity above 0.2 m/s (Figure 7, a3, b3 and c3).

Fish midline kinematics under four flow scenarios are depicted in Figure 8. The undulation amplitude of midlines in uniform flow for three species was the narrowest across four scenarios. Midlines undulation of P.R. and S.A. decreased when the fish passed through recirculation zones, mainstream zones and slots in turn, indicating that the variability in fish body decreased as the enhancement of hydrodynamics. The midline undulation of O.S. in the mainstream zones was basically equal to that in the slots (Figure 8b). Furthermore, based on the one‐way ANOVA results, the wavelength of each species was statistically different among the recirculation zones, mainstream zones, slots and uniform flow (P.R.: F = 23.35, p < 0.001; O.S.: F = 40.68, p < 0.001; S.A.: F = 33.06, p < 0.001), becoming progressively shorter under the above sequence of conditions. Only the wavelength of O.S. (1.1 BL) exceeded its body length at recirculation zones, and the wavelength of S.A. under uniform flow (0.6 BL) was the shortest among the three species. Notably, no significant difference existed between the wavelength of P.R. at recirculation (0.89 BL) and mainstream zones (0.87 BL), as well as that of O.S. at mainstream zones (0.88 BL) and slots (0.9 BL).

FIGURE 8.

FIGURE 8

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Variation in midlines and wavelength for Procypris rabaudi (a), Onychostoma sima (b) and Squalidus argentatus (c) at different positions in the fishway. Lowercase letters indicate significant differences (p < 0.05) in wavelength for each species under four flow patterns.

3.4. Coupling hydrodynamics and fish behaviours in trajectory Tc‐T3

The high‐proportion trajectory combination of Tc‐T3 served as the primary passage route across all species (Figure 5). Figures 9 and S4 illustrate this trajectory through a representative P.R. individual, showcasing a conserved passage strategy: (1) entry into pool‐1 through slot‐1 followed by sustained wall‐following behaviour (Figure 9a–d); (2) response to elevated total strain (3–18 s−1) near slot‐2 by redirecting into the mainstream with modified kinematics – increased tail‐beat frequency, decreased amplitude and angle – for rapid slot traversal (Figure 9e–g); (3) transition into recirculation zone‐2 (velocity = 0.08 m/s, TKE = 0.002 m2/s2, TS = 3 s−1) for energy conservation (Figure 9j); and (4) final reorientation and enhanced tail‐beat movement for slot‐3 passage.

FIGURE 9.

FIGURE 9

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Detailed illustration of a typical trajectory Tc‐T3 tracked by a single Procypris rabaudi under an inlet velocity of 0.3 m/s. Route Tc‐T3 was the typical trajectory for all rock carp with a proportion of 71.8% (Figure 5).

3.5. Retention behaviours in the fishway

Long‐term retention behaviours lasting a few seconds or a few minutes had an adverse impact on the chances of fish successfully passing through the fishways, which can be observed in both fish that successfully passed and those that did not. Fish typical retention behaviours were initially defined in this study (Figures 10 and S5). Fish were detained in slots where the mainstream zones met the recirculation zones, and they usually swam back and forth for short distances (Figure 10a). Their tail‐beat movements were restricted during this retention period. Fish were unable to flap their tail fins from low‐velocity zones to high‐velocity zones, and this tail‐beat process would stop until the body midline was in a straight line. Two different retention performances were observed in mainstream zones. One retention behaviour was that fish swimming direction intersected the mainstream direction (Figure 10, b1‐b2), and fish occasionally drifted with the mainstream but maintained a stiff body shape. Another retention behaviour was that fish swam against the mainstream (Figure 10, b3‐b4) with high intensity tail‐beat movement (10.26 Hz, Table S3). The retention behaviours in recirculation zones were relatively common and longer due to the presences of low velocity, TKE and TS (Figure 10, c1). Besides, fish can swim in a direction parallel to the baffles in recirculation zones but used their tail fins to constantly perceive the high velocity in mainstream zones (Figure 10, c2). Similarly, fish slowly swam with weak tail‐beat movement in recirculation zones while they attempted to approach the mainstream using the tail fin (Figure 10, c3). Fish maintaining static with the current was frequently observed in recirculation zones; their swimming direction was consistent with the velocity vector direction (Figure 10, c4).

FIGURE 10.

FIGURE 10

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Typical retention behaviours of Squalidus argentatus (S.A.) at slots (a), mainstream zones (b) and recirculation zones (c), respectively. Turning (d) and milling (e) retention behaviours of an individual S.A. among three positions.

In addition to the retention behaviours at three specific positions, fish exhibited turning and milling retention behaviour interspersed among the three positions (Figure 10d,e). Fish turning retention behaviour of rotating the body at large angles was frequently observed in recirculation zones. Fish swam with the current in recirculation zones, then gradually switched their swimming direction until they swam in a direction parallel to baffles (Figure 10, d1‐d5). At that moment, fish body had completed a 90‐degree rotation. Once fish perceived the high‐velocity or obvious velocity gradient near the mainstream zones, fish body was severely curved to avoid the high‐intensity hydrodynamics zones and continued to rotate their bodies for maintaining a comfortable swimming status (Figure 10, d6‐d7) until they finished this turning retention behaviour (Figure 10, d8).

Furthermore, fish milling retention behaviour occurred among slots, recirculation zones and mainstream zones. When fish approached the mainstream adjacent to slot‐2 (Figure 10, e1), they would follow the mainstream and drifted to the centre of mainstream (Figure 10, e2‐e4). Then, fish returned to the recirculation zones (Figure 10, e5) and swam in a direction consistent with current to the slot‐2 again (Figure 10, e6‐e7). During this milling period, fish swimming direction was basically intersected with the mainstream direction, with no significant body bending, as observed in turning retention behaviour. The trajectory of milling retention behaviour was a quasi‐circular route or a quasi‐elliptic if they drifted to slot‐3 rather than the mainstream centre. Finally, fish would start from the slot‐2 again to begin the next milling retention behaviour (Figure 10, e8). The swimming direction of fish in milling behaviour didn't change too much. Compared to fish turning retention behaviour, the zones covered by the milling retention behaviour were broader.

4. DISCUSSION

4.1. The relationship between hydrodynamics and trajectory in the fishway

Previous studies have categorized fish trajectories in the vertical slot fishway to two trajectories specific to recirculation zones and one trajectory specific to mainstream zones (Calles & Greenberg, 2007; Shi et al., 2024; Wang et al., 2010). However, few studies chose to quantify the hydrodynamic characteristics of each trajectory, most of them regarded the hydrodynamics of the regions where these trajectories located as the hydrodynamics of these trajectories. Sudden variations in hydrodynamic characteristics, such as the TS changing from high‐to‐low‐velocity zones and the presence of vertical slots, can contribute to fish failing to pass through fishways. Thus, this study quantified the hydrodynamic characteristics and hydraulic complexity of each typical trajectory, which can further explain the mechanism of why fish selected a specific trajectory as their primary upstream trajectories in the fishway (Katopodis et al., 2019; Zheng et al., 2022). Our study revealed vital insights demonstrating the relationship between fish energy benefits and trajectory distribution in VSF, which provided a novel framework to evaluate fishway passage efficiency.

Our study (swimming preference in Figure 4 and trajectory routes in Figure 5) supported that fish preferred to swim in the area with low‐intensity hydrodynamic characteristics to pass through the fishway (Castro‐Santos et al., 2017; Silva et al., 2018) and selected the trajectory where the energy cost was relatively lower (Kanter & Coombs, 2003; Williams et al., 2012). Low velocity, TKE, TS and wall effect in recirculation zones provided adequate resting opportunities for fish upstream swimming. In this research, the trajectory combination of Tc‐T3 in recirculation zones can further confirm this fact. In pool‐1, the low willingness of fish to select trajectory Tb as the primary forward route can be attributed to the high velocity along this trajectory. For the selection of Ta or Tc to pass through pool‐1, this presents a question: why different choices were made for the two trajectories belonging to the recirculation zones after fish passed through slot‐1. One possible reason may be related to the hydrodynamic differences between the two trajectories: the flow direction in Tc, which is completely opposite to the direction of fish movement, was more conducive to fish swimming against current with positive rheotaxis (Silva et al., 2020; Vowles et al., 2014). Besides, low velocity and complex TS of Tc (Figure 6, a2 and c2) attracted fish to move upstream by creating a low‐intensity hydrodynamic environment. Energy benefit of Tc also can be another explanation. Fish can obtain more kinetic energy when they swam with Tc to reduce their own energy consumption (Silva et al., 2012) from the results of M 2 (Figure 6, d2).

Particularly, trajectory T1 in recirculation zone‐1 was the only trajectory without a straight‐line segment in all recirculation zones. Fish swam against the relatively strong drag force (M 1 = 0.33 J/kg·m, Figure 6, d1) provided by the mainstream after passing through slot‐2 due to their positive rheotaxis and body inertia, causing that more individuals naturally swam away from the long baffle area in recirculation zone‐1. Phenomenon that fish swam along the long baffle to enter recirculation zone‐1 was seldom observed during testing. Thus, the effects of side walls and baffles in recirculation zone‐1 on the T1 profile were limited. In general, the spatial distribution of upstream trajectory was independent of fish species; selecting areas with low hydrodynamic intensity within pools to pass through fishways may represent a natural reaction of fish.

4.2. Fish swimming kinematics in the fishway

This study quantified fish swimming behaviours in vertical slot fishway by calculating tail‐beat kinematics metrics, midline kinematics and wavelength. Based on existing research achievements, low‐intensity hydrodynamics generated low‐intensity tail‐beat movement (Kucukali et al., 2022; van Weerden et al., 2014). Thus, the tail‐beat frequency of the three species in recirculation zones was the lowest compared to that in other conditions. The velocity in mainstream was larger than that of uniform flow under the same outlet velocity. However, fish tail‐beat frequency under uniform flow was significantly higher than that in the mainstream zones, indicating lower energy expenditure for fish swimming in the mainstream. The fact of high flow velocity but low energy expenditure was not consistent with the conclusions from previous studies, which can be attributed to the TS and TKE distributions in the fishway. The presence of slot‐2 enriched the TKE gradient across the entire mainstream under outlet velocity above 0.3 m/s (Figure 3c), and low TKE area in the mainstream zone provided extra opportunities for fish to decrease their tail‐beat frequency. Besides, differences in TS distribution of the two flow patterns may have the potential to influence fish tail‐beat movement. The obvious TS variation in uniform flow occurred near the side walls and covered a tiny area, whereas the low TS value ran through the middle of mainstream. Low TS in mainstream zones may be beneficial for reducing energy cost during fish tail‐beat movement. Interestingly, the tail‐beat movement of O.S. was stronger in the mainstream zones than at the slots, a pattern distinct from the other two species that suggests a unique behavioural strategy. As an endemic benthic species thriving in rapid flows (Zhong, 2008), its elevated activity in the mainstream may represent an active energy investment in flow exploration and habitat selection, rather than a direct transit behaviour. This species might be utilizing its strong swimming capability to thoroughly assess the hydraulic environment, a behaviour that is less pronounced in the constricted, pass‐through flow of the slots. Consequently, its kinematics reflect not only the hydraulic demand of locomotion but also a species‐specific exploratory behaviour in favourable flow conditions, leading to greater tail‐beat effort in the open mainstream than in the confined slots.

Midline kinematics of three species reflected the responses of body oscillation amplitude to different flow patterns, and their head amplitude changed a little across four flow patterns. Fish midline kinematics was strongly associated with their body shape (Duponchelle et al., 2021; Smits, 2019). In this study, the body shapes of all three species belonged to spindle type; however, several differences still existed among them. The body height and the ratio of height to length (H/L) of P.R. were the highest; this characteristic allowed its rigid body section to be longer, contributing to a relatively weaker degree of body oscillation. Combined with the results of tail‐beat kinematics, the midline kinematics of S.A. was the most vulnerable to the change of flow patterns. S.A., with the smallest H/L value among the three species, possesses a much slender body shape and a smoother dorsal line; this body characteristic enables greater body deformation to encounter various flow patterns.

4.3. Further discussion

The definition and occurrence mechanism of retention behaviours in fishway were seldom reported in previous studies, and this study defined five types of retention behaviours at different positions in the fishway. Fish tail‐beat movement was not very intense during retention, such as large tail‐beat amplitude with low frequency, indicating that fish in retention behaviours spent less energy to maintain continuous swimming (Li et al., 2021). Therefore, the presence of retention behaviours was not only harmful to the target fish species but also can be regarded as an alternative to rest. However, long‐term retention behaviours without fish fatigue would prolong passage time and decrease fishway efficiency (Shi, Li, et al., 2022a). It is necessary to reduce the occurrence frequency of fish retention behaviours for enhancing the passage rate of fishways. The most direct method to avoid retention behaviours is to reduce the area of recirculation zones. In this study, the area of recirculation zone‐3 where Ta was located was larger than the area of recirculation zone‐4 where Tc was located, leading to the long‐term retention behaviour and further decreasing the success rate of fish passing through the slots along Ta. However, considering that the fish species and number to be accommodated in a fishway are quite large, reducing the area of the recirculation zone may be unrealistic.

We have observed that the status of fish in retention behaviours was relatively relaxed due to their less‐intense tail‐beat movement; stimulating this relaxed status to another positive swimming status by introducing more flow patterns in fishways can be a key concept to decrease the occurrence frequency of retention behaviours. Flow patterns can be modified without altering the dimensions of baffles or side walls by incorporating physical structures (Kemp & O'Hanley, 2010), such as cylinders of various sizes or miniature riffle‐pool sequences. Introducing subtle flow disturbances or structures in these zones could encourage continued upstream movement without significantly increasing energy costs. Further comparative experiments should be carried out to improve the hydrodynamic characteristics of fishways and enhance the passage efficiency of fishways.

5. CONCLUSIONS

This study analysed the trajectory distribution, swimming kinematics and behaviour of three fish species in a vertical slot fishway. We found that increasing the outlet velocity widened the mainstream zones and constricted the recirculation zones. Furthermore, the ordinary pool's high‐velocity zone profile was more curved than that of the outlet pool. Analysis of hydraulic complexity indicated that fish swimming along side walls and baffles in recirculation zones capitalized on greater kinetic energy, aiding their passage. Kinematic results showed the minimum tail‐beat frequency in recirculation zones. In contrast, the mainstream and slots elicited stronger tail‐beat movements, with uniform flow provoking the most intense activity due to its high frequency. A progressive decrease in body oscillation amplitude and wavelength was observed from recirculation zones to mainstream, slots and uniform flow. Additionally, five defined retention behaviours negatively impacted passage rate and time. Supportively, M 1 and M 2 results demonstrated that recirculation zones along walls provided more kinetic energy, and velocity gradients promoted trajectory formation. By integrating kinematics with trajectory hydrodynamics, this study elucidates fish swimming performance and offers valuable insights for enhancing fishway design and efficiency.

AUTHOR CONTRIBUTIONS

Xiaoming Yan: formal analysis, writing – original draft, conceptualization, investigation. Fei Liu: investigation, data curation, funding acquisition. Chenyang Cao: formal analysis, writing – original draft, conceptualization. Shikang Liu: conceptualization, investigation. Qihao Meng: formal analysis, software. Yuqian Xi: investigation, data curation. Lijian Ouyang: software, funding acquisition. Weiwei Yao: writing – review and editing, supervision, funding acquisition.

CONFLICT OF INTEREST STATEMENT

The authors declare no competing interest.

Supporting information

Table S1. Computational domain mesh characteristics.

Table S2. Number of routes chosen by fish at each flow velocity.

Table S3. Comparison of tail‐beat kinematics at the same position among three fish species.

Table S4. Comparison of swimming behavioural characteristics among fishes at each flow velocity.

Figure S1. The study area of this research. (a) Location of the Yangtze River basin in China. (b) Location of the Chishui River basin within the Yangtze River basin. (c) Chishui River basin and location of the text site (FX Town).

Figure S2. Comparison of measured and numerically simulated (a) flow velocity and (b) turbulent kinetic energy results.

Figure S3. Combined analysis of typical trajectories and hydrodynamic characteristics at 0.3 m/s outlet velocity. (a) Velocity distribution, (b) turbulent kinetic energy (TKE) and (c) total hydraulic strain (TS).

Figure S4. Detailed illustration of a typical trajectory‐TcT3 tracked by a single rock carp under inlet velocity of 0.3 m/s.

Figure S5. Typical retention behaviours of S.A. at slots (a), mainstream zones (b) and recirculation zones (c), respectively. The turning (d) and milling (e) retention behaviours of an individual S.A. among three positions.

JFB-108-2010-s001.docx (6.7MB, docx)

ACKNOWLEDGEMENTS

We are grateful for financial support from the National Key Research and Development Program of China (2022YFC3202002, 2023YFC3205900 and 2022YFB3206905). The Project of Xinjiang Ecological Water Conservancy Research Center (no.: 2024B002). The Guizhou Province Science and Technology Project [(2024)116]. The Science and Technology Project of Bijie city of open competition mechanism to select the best candidates [grant no.: BKHZDZX (2023)1]. Dongfeng Lake and Liuchong River Basin of Observation and Research Station of Guizhou Province [grant no.: QKHPT YWZ(2025)002]. Bijie Talent Team of Biological Protection and Ecological Restoration in Liuchong River Basin (no.: 202112). CWRH‐SCU PHD Student Innovation‐Fostering Fund (2026C02B1209).

DATA AVAILABILITY STATEMENT

All data used in this manuscript are included within the manuscript.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Table S1. Computational domain mesh characteristics.

Table S2. Number of routes chosen by fish at each flow velocity.

Table S3. Comparison of tail‐beat kinematics at the same position among three fish species.

Table S4. Comparison of swimming behavioural characteristics among fishes at each flow velocity.

Figure S1. The study area of this research. (a) Location of the Yangtze River basin in China. (b) Location of the Chishui River basin within the Yangtze River basin. (c) Chishui River basin and location of the text site (FX Town).

Figure S2. Comparison of measured and numerically simulated (a) flow velocity and (b) turbulent kinetic energy results.

Figure S3. Combined analysis of typical trajectories and hydrodynamic characteristics at 0.3 m/s outlet velocity. (a) Velocity distribution, (b) turbulent kinetic energy (TKE) and (c) total hydraulic strain (TS).

Figure S4. Detailed illustration of a typical trajectory‐TcT3 tracked by a single rock carp under inlet velocity of 0.3 m/s.

Figure S5. Typical retention behaviours of S.A. at slots (a), mainstream zones (b) and recirculation zones (c), respectively. The turning (d) and milling (e) retention behaviours of an individual S.A. among three positions.

JFB-108-2010-s001.docx (6.7MB, docx)

Data Availability Statement

All data used in this manuscript are included within the manuscript.

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