Momentum, Energy and Drag Coefficients for Ice‐covered Rivers

A lack of reliable hydraulic parameters has been a main factor hindering the progress in predicting ice‐covered river flows; the predictions need input hydraulic parameters such as the energy, momentum and drag coefficients (α, β and CD). In this paper, a large volume of winter measurements of flow velocity collected from 26 ice‐covered rivers is analysed to determine the coefficients. Using cross‐sectionally distributed streamwise velocities, α and β are evaluated directly. They are also derived from empirical relationships. For both the riverbed and ice cover, CD is evaluated on the basis of turbulent boundary‐layer theory and the quadratic law for friction. The results show that ice‐covered river flows feature a number of velocity distributions: a single core of high velocities in the thalweg, a single core of high velocities off the thalweg and multiple cores of relatively high velocities at the cross section. The velocity distributions are significantly non‐uniform. Direct evaluations give overall averages of α = 1.23 and β = 1.08. They represent 22% and 8.3% corrections to the literature values (overestimates). An examination of the velocity distributions reveals that the ratio of the maximum velocity to the cross‐sectionally averaged velocity equals 1.356. It is recommended that values of CD = 0.004 ± 0.0005 and 0.002 ± 0.0005 be used for the riverbed and ice, respectively. This paper discusses turbulence shear stress and the associated length scale in the boundary layer as well as winter discharges. The results have applications to aquatic ecology, water resources development and flood prevention.