A model for vertical frazil distribution

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Abstract
A model is presented for the evolution of frazil over depth and with time in a turbulent flow. The net upward migration due to buoyancy of the frazil is opposed by intermittent mixing induced by large energy‐containing eddies. A surface renewal model is used to describe the effects of large eddy mixing. Parameters that represent an entire water body are obtained by averaging those of discrete water columns using a probability density function. These parameters include the concentration profile, the surface age, and the surface layer thickness. A dimensionless surface renewal frequency characterizes the frazil distribution at equilibrium. The rate of heat loss from the water surface, the surface renewal frequency, and the critical surface layer thickness determine whether the frazil will evolve toward a well‐mixed equilibrium state or a layered state. The model provides a physical basis for understanding the transition between these states, consistent with existing empirical criteria and field data.