Theoretical and field-based analysis of lateral momentum flux in ice-covered streams

Ice cover introduces surface roughness and modifies the hydrodynamics of natural rivers, particularly influencing momentum redistribution and bed shear stress. Here, we discuss a theoretical basis for lateral momentum flux in ice-covered streams based on the depth-integrated Reynolds-Averaged Navier–Stokes equations. Field measurements were conducted during the winters of 2022–2025 in a meandering reach of the Red River of the North (Fargo, ND, USA), using an Acoustic Doppler Current Profiler (ADCP) to capture time- and depth-averaged flow velocities across four cross-sections. The model reveals that secondary flow and Reynolds stress contribute comparably to lateral momentum flux. Field observations indicate that the presence of ice suppresses the formation of coherent secondary flow cells. The model further demonstrates that lateral gradients of momentum flux are directly linked to variations in bed shear stress, suggesting a strong coupling between ice-modulated secondary circulation and near-bed dynamics.