Simulation of upstream behavior of Schizothorax wangchiachii in vertical slot fishway

Fishways are an important engineering measures designed to assist fish in migrating upstream over a dam. However, the initial construction of fishways does not consider the combination of hydraulic characteristics and fish behavior, leading to poor effectiveness. The optimization of fishway structure must evaluate the relationship between fish behavior and hydraulic factors. It is necessary to develop an effective mathematical model to simulate fish upstream migratory for exploring the relationship between fish behavior and hydraulic factors. In this study, a model for predicting upstream fish behavior considering multiple hydraulic factors and variable-speed swimming of Schizothorax wangchiachii was proposed, based on the behavior data of S. wangchiachii obtained from physical experiments and the Euler-Lagrangian-agent method (ELAM). The flow velocity, turbulent kinetic energy, vorticity, and strain rate were used as the key hydraulic factors driving fish movement. Firstly, principal component analysis was used to calculate the effects of flow velocity, turbulent kinetic energy, vorticity, and strain rate on the upstream behavior of S. wangchiachii. Next, the preference range of S. wangchiachii for these factors was determined through statistical analysis. Then, a fish behavior model was developed based on the characteristics of fish movement, it includes upstream behavior (the direction of fish movement is opposite to the direction of water flow), obstacle avoidance behavior (fish movement avoids obstacles during movement), inertia behavior(when the fish passes through the vertical seam, it will move forward some distance due to inertia), and random behavior (imitating the random movement of fish under natural conditions). Additionally, a variable fish swimming speed model was developed by analyzing the response relationship between water flow velocity and fish swimming speed. Finally, the proposed model was used to simulate the fish’s upstream trajectory in the vertical slot fishway. The characteristic trajectories of the both simulated and measured trajectories were calculated using a ninth-order polynomial regression model. These characteristic trajectories were then compared and analyzed to verify the model’s reliability. To further analyze the impact of vorticity, strain rate, flow velocity and turbulent kinetic energy on fish upstream behavior, four schemes of control experiments were designed. Control experiments were realized by removing the influence weight of vorticity, strain rate, turbulent kinetic energy, and flow velocity in the model, respectively and not changing the fish’s preference range of hydraulic factors. The experimental results indicate that S. wangchiachii has distinct preference ranges for flow velocity, turbulent kinetic energy, vorticity, and strain rate. The error between the characteristic trajectory of the simulated and measured trajectory is small (R² = 0.935, RMSE = 0.043), it suggests that the proposed model in this study can accurately predict the upstream behavior of S. wangchiachii in the fishway. Vorticity, strain rate, turbulent kinetic energy and flow velocity have different effects on the upstream behavior of S. wangchiachii. When the effects of vorticity, strain rate, turbulent kinetic energy and flow velocity on the fish upstream behavior are not considered respectively, the R² of the simulated trajectory and the measured trajectory are 0.526, 0.799, 0.861 and 0.910, respectively. Correspondingly, the RMSE values were 0.127, 0.09, 0.074, and 0.054, respectively. These errors are all lower than those observed in the original scheme. Therefore, the influence of the above four hydraulic factors on fish tracing can not be ignored. The weight coefficient of vorticity is 0.246, which is relatively small, but it plays a key role in the process of fish upstream to ensure that fish will not get lost. The fish upstream behavior prediction model proposed in this study provides a reference for designing and optimizing fishways.