The vertical concentration distribution of frazil-ice crystals in a stream during the formation and growth of frazil ice was discussed in a preliminary way by Gosink and Osterkamp (1981). This paper extends and completes the analysis of buoyant rise velocities of frazil-ice crystals and applies the results to an interpretation of measured velocity profiles in rivers during frazil-ice events. Additional experimental data are also presented. Two time scales are defined: the buoyant time scale TB, which represents the time required for a frazil crystal to rise, buoyantly, from the river bottom to the water surface, and the diffusive tine scale TD, which represents the time required for a frazil crystal to he transported by turbulence through the depth. It is shown that the ratio of the time scales TB/TD defines the nature of the layering processes; in particular, if TB/TD<1, then buoyant forces Till lift a frazil crystal faster than turbulent diffusion can redistribute it and the flow will be layered. Conversely, if TB./TD>1, turbulent mixing will proceed faster than buoyant lifting and the flow will be well-mixed. This ratio, for frazil particles of diameter 2 mm or more, corresponds to rule-of-thumb velocity criteria developed in Norway and Canada to distinguish layered frazil-ice/water flow from well-mixed flow.
The development of this theory depends in large part upon the determination of TB, which depends upon the rise velocity of frazil-ice crystals. A force balance .nodel was developed for the rise velocity of a frazil crystal. Field observations during frazil -ice formation in Goldstream Creek and in the Chatanika River north of Fairbanks are reported, including a series of measurements of the rise velocities of frazil-ice crystals. Typical particle size of frazil ice was about 2 mm with a rise velocity of about 10.0 mm s -1. The agreement of measured rise velocities with the theoretical model is good considering uncertainties in the drag coefficient and in the determination of frazil crystal sizes under field conditions.
Velocity profiles in the Chatanika River and in Goldstream Creek during frazil formation suggest that the time-scale ratio may serve as a transition criterion between layered frazil-ice/water flow and well-mixed flow. This ratio was calculated with the rise velocity of frazil-ice crystals arbitrarily chosen to be 0.01 m s−1.