Modeling fish swimming trajectories in a sudden expansion flow based on eulerian lagrangian agent method (ELAM): A case study of red crucian carp

Based on the experimental data of Red Crucian Carp swimming in a sudden expansion flow, this study established a fish swimming trajectory prediction model using the Eulerian–Lagrangian–agent method (ELAM). Considering the observed phenomenon that fish may exhibit different swimming behaviors under identical hydrodynamic conditions in both real-world and experiments, we innovativily summarize that fish may randomly adopt two distinct behavioral strategies: aggressive and conservative navigation in various environments. Through a systematic analysis of the experimental results of fish swimming trajectories and the numerical simulation results of the sudden expansion flow, we quantified the preferred value range and sensitivity of fish to the key hydraulic parameters (including flow velocity, turbulent kinetic energy, and strain rate) under each strategies. Based on these findings, we constructed a trajectories prediction model for fish swimming in complex flow conditions within the ELAM framework, which incorporates real-time hydrodynamic feedback mechanisms. This model is then used to simulate and analyze the swimming trajectories of Red Crucian Carp of three different body sizes in sudden expansion flows with inlet velocities ranging from 0.2 to 1.0 m/s. The results demonstrate that the prediction model successfully replicates the four typical trajectory patterns observed in the experiments, namely Main Current Migration, Recirculation Bypass Migration, Corner Retention, and Failed Migration. Moreover, the predicted trajectories' dependence on fish size and flow velocity aligns well with the experimental results. The model developed in this study can effectively capture the interaction between the fish and the surrounding flow, enable the prediction of the success rate and the efficiency of fish navigating through complex flow fields, which offers a potential alternative to traditional fish passage experiments, thereby providing a valuable tool for the design and optimization of fish protection measures.