The effect of ‘hydraulic-visual’ interaction on the intensity of fish schooling in the upstream movement of juvenile silver carp

Understanding how hydraulic and visual factors jointly regulate fish schooling is critical for improving fish passage performance. Using juvenile silver carp (Hypophthalmichthys molitrix) as model organisms, this study investigated how schooling intensity responds to combined effects of flow velocity, turbulence kinetic energy, and visual guidance cues from obstacles. Controlled flume experiments with fixed group size (five individuals) were conducted under three flow conditions. By integrating simulated hydraulic fields with spatial patterns of schooling intensity and swimming energy expenditure, relationships among flow characteristics, energetic demand, and schooling behaviour during upstream movement were quantitatively analysed. The results showed that: (1) increasing flow velocity constrained lateral exploration and prompted aggregation within the main flow corridor, leading fish to ascend predominantly along the principal flow direction ; (2) under relatively mild flow conditions, turbulence kinetic energy alone exerted a limited influence on schooling intensity, whereas in obstacle zones where high velocity co-occurred with low turbulence, fish preferentially selected a high-velocity corridor as an “efficient passage”; (3) increases in short-term or cumulative energy expenditure were not, by themselves, sufficient to elicit schooling, but rapid surges in energetic demand when encountering high-velocity barriers were associated with enhanced group cohesion; (4) after passing velocity barriers, fish adopted short-burst acceleration strategy in low-velocity, low-turbulence regions upstream of obstacles to avoid re-forming dense schools, indicating an active tendency to reduce prolonged energy costs when possible; and (5) obstacles provided salient visual cues that helped fish avoid collisions and adjust their movement direction during rapid upstream swimming. Overall, these findings demonstrate that schooling intensity is a dynamic behavioural adjustment shaped by the combined effects of hydraulic constraints, energetic demands, and visual information. The results provide mechanistic insight into collective upstream migration and offer practical guidance for the hydraulic and structural optimisation of fish passages.