This paper presents the formulation, numerical method, and field applications of a numerical model for dynamic transport and jamming of surface ice in rivers. The model considers the ice as a continuum. The internal ice resistance is described by a viscous-plastic constitutive law, in which the pressure term is formulated by modifying the Coulomb type constitutive relationship for static ice jams. The partial slip boundary condition for ice along solid boundaries is treated by the method of images. The effect of bed resistance on grounded ice is considered. The hydrodynamic component of the model uses an Eulerian finite-element method, while the ice dynamic component uses a Lagrangian discrete parcel method based on the smoothed particle hydrodynamics. The model has been applied to and verified with several idealized and field problems. The scaling laws for ice dynamics are discussed.
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