Theoretical Model of River Ice Jams

A mathematical analysis is developed to describe the evolution and characteristics of river ice jams. The principal components of the analytical model are the static force equilibrium of the fragmented ice cover; the unsteady continuity equations for the frozen and liquid water; the nonuniform unsteady momentum relation for the flow; and relations in which compressive and shear strengths of the floating fragmented ice cover vary linearly with local jam thickness. A numerical method is outlined for solving the equations for the case in which the jam has evolved to the point that it propagates upstream with constant velocity (quasi-steady conditions), and a complete set of example results is presented for a specific flow and channel. Estimates are derived for the time required for the jam to evolve to the quasi-steady state and for the velocity of the jam front during the evolutionary stage.