Analytical model for the suspended sediment concentration in the ice-covered alluvial channels

Ice cover formed on an alluvial channel can significantly alter the flow characteristics, such as the vertical distributions of streamwise velocity and shear stress, and hence the water and sediment transport process. The vertical profile of the suspended sediment concentration in the ice-covered alluvial channels with steady uniform flows is investigated in this study. To calculate the suspended sediment concentration, we are based on the Schmidt O'Brien equation and deduce an analytical model that employs an existing eddy viscosity model and a modified formula of the sediment fall velocity considering the common effects of the upper and lower boundaries. The proposed analytical model is then validated by using available experimental data reported in the literature. The predicted accuracy of the proposed model is evaluated through error statistics by comparing to previous modeled results. The relative concentration profiles of the suspended sediment are subsequently simulated by applying the validated analytical model with different characteristic parameters. Results show that the relative concentration decreases with the increase of both the ice cover roughness and the sediment fall velocity. The uniformity of the relative concentration distribution is closely related to the value of the proportionality parameter sigma, revealing the physical mechanism that the more prominent the turbulent diffusion effect is, the more uniform the relative concentration profile is.