Introduction
The construction of numerous regulating dams and weirs has resulted in detrimental impacts on the ecosystem and aquatic life. Temporary and diversion dams built in river sections impact aquatic organisms, particularly fish, and are crucial for their reproduction and spawning activities. Varying depths of water flow both upstream and downstream of the dams affect fish migration across different seasons; thus, a fish pass structure is essential to facilitate this movement. The design of such a structure must be informed by a comprehensive understanding of the swimming behaviors of aquatic species (Kim et al., 2015; Shahabi et al., 2022). Turbulent flow conditions diminish the swimming speed of fish and can lead to injuries. Fish exhibit stable, continuous, and explosive swimming speeds, which range from minimum to maximum values, respectively (Beamish, 1978). Consequently, it is vital to possess knowledge of the physics and hydraulics of flow, as well as the geometry of fishway structures. The geometry of these structures can take forms such as rectangular, circular, and elliptical, and they function as weir fishway for water transport (Rajaratnam et al., 1991; Duguay & Lacey, 2015). The design of fishway structures that incorporate lateral barriers and weirs enhances roughness, reduces flow velocity, and positively influences the movement of aquatic organisms. Studies on weir fishway featuring continuous slotted barriers have indicated that flow depth is contingent upon hydraulic parameters such as discharge, slope.

Methodology
To conduct this research and examine the scenarios under consideration, the parameters influencing the flow through the spillway and the barriers utilized in the fishway structure are introduced in accordance with equation (1). Subsequently, by Buckingham P-theory, dimensionless parameters are derived as per equation (2), which include: Froude number, Reynolds number, relative depth, dimensionless discharge, Darcy-Weisbach coefficient, and bottom slope. Given the constant width of the waterway, apex angle, height of barriers, and their respective distances, the variables were eliminated, leading to the formulation of the following equation (2). In this study, the fishway structure is designed in a W-weir, as illustrated in Figure 1. To enhance the efficiency of the structure and analyze the spillway type fishway, the configuration of fixed barriers is taken into account. The outcomes of this numerical modeling were juxtaposed with the findings from the modeling of the W-weir fishway in the study conducted by Shahabi et al. (2022), and the results were critically evaluated. The laboratory model is depicted in Figure 2, and the physical experiments referenced in the aforementioned research were executed within this flume. This research investigates the hydrodynamic conditions of the fishway structure, characterized by a fixed opening angle and relative distance of the weir.
Results and Discussion
In accordance with the simulation scenarios presented in Table 1, the results of this study have been meticulously analyzed and assessed in alignment with the research objectives. This section evaluates the velocity patterns within the structure, flow resistance, the impact of the Froude number, and turbulent kinetic energy, each of which is elaborated upon in the following sections. The variations in velocity are illustrated in two dimensions: the length and width of the channel. The numerical values and their trends are shown in Figure 3. As a result, at a slope of 7%, the peak velocities for flow rates of 20 liters per second and 43 liters per second are recorded at 1.67 m/s and 1.93 m/s, respectively, while the minimum velocities, affected by the presence of obstacles, are 0.64 m/s and 0.7 m/s, respectively, observed in the opposing direction of the flow. As depicted in Figure 6, an increase in the Froude number is associated with a reduction in energy loss coefficients, which is attributed to the increase in depth and the decrease in the effects of spillway barriers and their roughness. The numerical values for friction loss coefficients and Manning roughness at different slopes are illustrated in Figures 6 and 7, respectively. As the slope rises from 4% to 10%, the root coefficient of friction for the structure at the Froude number is recorded at 0.44, with the highest value reaching 0.95 for the maximum Froude number, while the lowest value, at a slope of 4%, is 0.27, corresponding to 0.9.
Conclusion
The flow dynamics observed in the three-dimensional velocity distribution along the fishway structure, which incorporates a W-weir fishway, demonstrated the emergence of vertical vortices downstream of the structures, alongside notable pressure fluctuations. The results indicated that an increase in the Froud number corresponded with a reduction in flow resistance. Furthermore, as the Froud number rose, both the Manning roughness coefficients and the Mody friction coefficients showed a decline. In summary, the findings offer valuable insights into the effects of the structure employed in this study. At the maximum slope of 4%, the structure exhibited enhanced performance, fostering significantly more favorable conditions for fish migration. The analysis of the three-dimensional flow velocity along the structure, taking into account the influence of spillway kinetic energy on the vertical vortices generated in the downstream slope, revealed that vertical vortices are indeed formed downstream of the structures, with the performance of the structure at a 4% slope being more advantageous compared to the other slopes.
Keywords: Kinetic energy, Reynolds shear stress, Froude number, Flow resistance.
Introduction
The construction of numerous regulating dams and weirs has resulted in detrimental impacts on the ecosystem and aquatic life. Temporary and diversion dams built in river sections influence aquatic organisms, particularly fish, and are crucial for their reproduction and spawning activities. The varying depths of water flow both upstream and downstream of the dams affect fish migration across different seasons; thus, a fish pass structure is essential to facilitate this movement. The design of such a structure must be informed by a comprehensive understanding of the swimming behaviors of aquatic species (Kim et al., 2015; Shahabi et al., 2022). Turbulent flow conditions diminish the swimming speed of fish and can lead to injuries. Fish exhibit stable, continuous, and explosive swimming speeds, which range from minimum to maximum values, respectively (Beamish, 1978). Consequently, it is vital to possess knowledge of the physics and hydraulics of flow, as well as the geometry of fishway structures. The geometry of these structures can take forms such as rectangular, circular, and elliptical, and they function as culvert structures for water transport (Rajaratnam et al., 1991; Duguay & Lacey, 2015). The design of fishway structures that incorporate lateral barriers and weirs enhances roughness, reduces flow velocity, and positively influences the movement of aquatic organisms. Studies on culverts featuring continuous slotted barriers have indicated that flow depth is contingent upon hydraulic parameters such as discharge, slope.
Methodology
To conduct this research and examine the scenarios under consideration, the parameters influencing the flow through the spillway and the barriers utilized in the fishway structure are introduced in accordance with equation (1). Subsequently, by Buckingham P-theory, dimensionless parameters are derived as per equation (2), which include: Froude number, Reynolds number, relative depth, dimensionless discharge, Darcy-Weisbach coefficient, and bottom slope. Given the constant width of the waterway, apex angle, height of barriers, and their respective distances, the variables were eliminated, leading to the formulation of the following equation (2). In this study, the fishway structure is designed in a W-shape, as illustrated in Figure 1. To enhance the efficiency of the structure and analyze the spillway type fishway, the configuration of fixed barriers is taken into account. The outcomes of this numerical modeling were juxtaposed with the findings from the modeling of the W-shaped spillway type fishway in the study conducted by Shahabi et al. (2022), and the results were critically evaluated. The laboratory model is depicted in Figure 2, and the physical experiments referenced in the aforementioned research were executed within this flume. This research investigates the hydrodynamic conditions of the fishway structure, characterized by a fixed opening angle and relative distance of the spillways. The number of parameters and specifics of the experiment are detailed in Table 1.
Results and Discussion
Based on the simulation scenarios outlined in Table 1, the findings of this research have been thoroughly analyzed and evaluated in line with the research objectives. This section assesses the velocity pattern within the structure, flow resistance, the influence of the Froude number, and turbulent kinetic energy, each of which is discussed in detail below. The variations in velocity are depicted in two dimensions: length and width of the channel. The numerical values and their trends are presented in Figure 3. Consequently, at a slope of 7%, the maximum velocities for flow rates of 20 liters per second and 43 liters per second are recorded at 1.67 m/s and 1.93 m/s, respectively, while the minimum velocities, influenced by the presence of obstacles, are 0.64 m/s and 0.7 m/s, respectively, noted in the flow's opposing direction. As illustrated in Figure 6, an increase in the Froude number correlates with a decrease in energy loss coefficients, attributed to the increase in depth and the reduction of spillway barrier effects and their roughness. The numerical values for friction loss coefficients and Manning roughness at various slopes are depicted in Figures 6 and 7, respectively. As the slope increases from 4% to 10%, the root coefficient of friction for the structure at the Froude number is recorded at 0.44, with the highest value at 0.95 for the maximum Froude number, while the lowest value, at a slope of 4%, is 0.27, equating to 0.9.
Conclusion
The flow dynamics within the 3D velocity distribution along the fishway structure featuring a W-shaped spillway revealed the formation of vertical vortices downstream of the structures, accompanied by significant pressure fluctuations. The findings indicated that as the Froud number increased, the flow resistance diminished. Additionally, with the rise in the Froud number, both the Manning roughness coefficients and the Mody friction coefficients exhibited a decrease. Overall, the results obtained provide insight into the impact of the structure utilized in this investigation. At the maximum slope of 4%, the structure demonstrated superior performance, creating significantly more conducive conditions for fish migration.