Research on velocity distribution models in compound channels based on modified Tsallis entropy and Renyi entropy

Accurately understanding the velocity distribution in compound channels is of great theoretical and engineering significance, as it enhances the calculation accuracy of hydraulic parameters, improves simulations of sediment transport, and supports ecological restoration projects. This study focuses on a compound channel with a deep main channel and symmetric two-layered floodplains. By incorporating the composite momentum thickness, eddy viscosity coefficient, and velocity inflection point into the Tsallis and Renyi entropy frameworks, an improved cumulative distribution function is derived. This model effectively captures the abrupt changes in the velocity profile resulting from the effects of secondary flows and shear layers. Furthermore, by analyzing the intrinsic relationship between the momentum thickness of the mixing layer and the flow characteristics, a quantitative correlation with the dimensionless hydraulic parameter (Fr/Dr) was established, thereby enhancing the model's overall capability to describe complex flow structures. Research results indicate that both entropy-based models demonstrate satisfactory performance in predicting the depth-averaged velocity within both the main channel and the floodplain. However, the modified Tsallis entropy model exhibits superior predictive accuracy and stability under high-velocity gradient conditions in the floodplain and during high-discharge scenarios. This study provides a novel theoretical approach for predicting flow velocity distributions in complex cross-sectional morphologies, and offers a scientific basis for hydraulic computations and comprehensive river regulation in practical engineering applications.