Analytical solution for the vertical distribution of the longitudinal time-averaged velocity in ice-covered channel based on the eddy viscosity model

The existence of ice cover significantly changes the flow structure of the river, wherein the vertical distribution of the streamwise velocity is parabola with respect to the zero shear stress plane. Given that accurately predicting the velocity distribution is the basis of calculating the flow discharge, the sediment transport rate, and the bed evolution for ice-covered channels, an analytical solution for the vertical distribution of the longitudinal time-averaged velocity in ice-covered channels, which has a clear physical meaning and continuous velocity gradient, was derived by applying the two-layer hypothesis and the eddy viscosity model. Meanwhile, the application conditions of the frequently used log-law velocity formula and two-power law velocity formula were clarified. By using available experimental data and field data reported in the literature, the validity and accuracy of the analytical formula presented here were then compared with that of the existing log-law velocity formula and two-power law velocity formula. Based on the validated analytical formula, the sensitivity of the vertical distribution of the longitudinal time-averaged velocity to the physical characteristic parameters was also explored. The results show that the calculated values of the streamwise velocity by the presented analytical formula are in good agreement with the measured data and have higher accuracy than that of the log-law formula and the two-power law formula. Sensitivity analysis displays that the Reynolds number has little influence on the vertical distribution of the longitudinal time-averaged velocity, whereas the vertical distribution of the velocity is sensitive to the relative value of the ice cover roughness and the channel bed roughness. The maximum value of the longitudinal time-averaged velocity tends to the smooth boundary. These results are consistent with previous numerical results obtained by the k- s turbulence model, which again confirms the validity of the presented analytical solution. © 2023 International Research and Training Center on Erosion and Sedimentation and China Water and Power Press. All rights reserved.