On the depth-averaged models of ice-covered flows

Abstract

Impact of ice coverage is significant in controlling the depth-averaged velocity profile and influencing morphological processes in alluvial channels. However, this impact is largely unknown under field conditions. In this work, a numerical method is introduced to compute the depth-averaged velocity profile in irregular cross-sections of ice-covered flows, based on the Shiono-Knight approach. The momentum equation is modified to account for the presence of secondary flows and the ice coverage. The equations are discretized and solved with velocity boundary conditions at the bank and at one vertical. Our approach only requires the cross-section geometry and a single velocity measurement near the high-velocity region, offering a significant advantage in inaccessible locations by avoiding the need to measure the velocity profile in the entire cross-section. The proposed model is then validated using depth-averaged velocity profile and secondary flow patterns from laboratory observations, analytical solution, and Large-Eddy Simulation. Finally, the method is applied to infer depth-averaged velocity profiles in the Red River of the North, United States, to test its performance in meandering sections. The proposed method demonstrates its robustness in reconstructing flow profiles in ice-covered conditions with a minimal amount of available data, which is crucial for assessing erosion risks and managing spring floods in cold regions.