Analysis of river ice motion near a breaking front
Dynamic river ice breakup displays different behaviors depending on the physical characteristics of the river, the flow, and the ice cover. Although a quantitative theory of dynamic breakup is not yet available, one of the essential components of such a theory will be a description of the ice motion near the breaking front. In this paper we develop an analysis of this motion for a specific case. The analysis is generalized by allowing the speed of the breaking front to vary, and the parameters of the ice motion that are obtained represent different dynamic breakup behaviors that have been previously described. The results of the analysis include (i) the ice velocity, ice acceleration, and bank resistance at each point in a river reach as functions of time, (ii) the equilibrium ice velocity as a function of bank resistance and the ice velocity as a function of time for several initial and bank resistance conditions, and (iii) the time of ice motion, ice velocity, ice acceleration, and the convergence of the moving ice with distance from the breaking front. The measure of ice convergence quantifies the loss of surface area by the sheet required for ice continuity, and distinguishes the basic types of dynamic breakup. Key words: breaking front, dynamic ice breakup, ice continuity, ice convergence, ice motion, river ice.