On the structures of the ice-covered flows in a bend

Hydrodynamics of ice-covered rivers is a classical problem of turbulent flows. Due to the differences in the roughness of the ice and the bed layer, two sets of velocity and length scales exist in this flow. The classical theory suggests that these velocity and length scales warrant a double log-law profile where the logarithmic layers exist both near the bed and the ice layers. In this study, we examine the theoretical bounds for these logarithmic layers as 0.26 Re_τ^1/2 ≤ z⁺ ≤ 0.15 Re_τ with the Reτ → 200,000 in a river reach of the Red River in Fargo, North Dakota. Field surveys are conducted the Acoustic Doppler Current Profiler (ADCP - Sontek M9) in fixed-vessel deployment mode under ice-covered and open surface condition. In the bed layer, our measured data under open surface and ice-covered conditions show that the separation from the upper bound of the logarithmic region reaches z⁺ ≈ 10⁴. In the ice layer, the extension of the logarithmic region is only limited up to z⁺ ≈ 3 χ 10³. Therefore, the logarithmic layer of the ice layer does not follow the theoretical bounds. An alternative formulation for the velocity profile will be discussed and compared with the double log-law hypothesis.