Velocity estimation in compound channels with different bank slopes using Renyi and Tsallis entropy

The essential information required by hydraulic engineers for estimating the stage and discharge characteristics of open channels is a comprehension of velocity distribution. The current work employed time-averaged normalized velocity as a random variable in Tsallis and Renyi entropy-based model to construct velocity estimations in compound channels with varying bank slopes. According to the approach, both entropies should be maximized using the maximum entropy principle, with certain restrictions. Two Lagrange multipliers for Renyi entropy and dimensionless parameter G for Tsallis entropy must be derived for the model, and these quantities can be determined using average and maximum experimental velocity data. Laboratory measurements were used by considering 45 degrees and 90 degrees bank angle compound channels and to evaluate the velocity distributions, which were then contrasted with predicted velocity distributions by Renyi and Tsallis entropy methods. The resulting velocity profile matches the experimental data with great accuracy, mainly in the floodplain and main channel domains. However, the accuracy is less in and around slopes because of the nonuniform cross-section and involvement of secondary currents, ultimately affecting the velocity profile. This entropy-based velocity estimation in compound channels should open the way for the future inclusion of vegetation for a better understanding of flow in actual field circumstances.

Automated summary

The study focuses on the estimation of velocity distribution in compound channels with varying bank slopes, using the Tsallis and Renyi entropy-based model. The model maximizes both entropies with certain restrictions and derived Lagrange multipliers and parameter G. Experimental data from laboratory measurements were used to evaluate the velocity distributions and compared with the predictions by the entropy methods. Results show accurate velocity profiles in floodplain and main channel domains, while less accuracy is observed near slopes due to nonuniform cross-section and secondary currents. This entropy-based velocity estimation allows for a better understanding of flow in compound channels, with potential future inclusion of vegetation in field circumstances.