Two-dimensional numerical modelling of river ice dynamics

A two-dimensional numerical model is developed for the simulations of ice dynamics and hydrodynamics of rivers and lakes. The hydrodynamics component includes two models. For the first one, a single-water-layer model, a set of shallow water wave equations for the water flow underneath the surface ice are solved. The water flow in the surface ice layer is lumped to the water flow underneath it. For the second one, a two-water-layer model, two sets of shallow water wave equations are solved. One set is for the water flow below the ice-water interface, and the other is for the water flow in the surface ice layer. A finite element method is used to solve the hydrodynamic equations. The ice dynamic equations are solved by a Lagrangian discrete parcel method based on smoothed particle hydrodynamics (SPH). An instability analysis for SPH method is performed. A nonlinear viscous-plastic constitutive model is adopted to compute the internal stresses of rubble ice for large strain rates, and a nonlinear elastic-plastic constitutive model is proposed for the computations of the internal stresses for small strain rates. The components of hydrodynamics and ice dynamics are coupled through the interactions between the surface ice and the water flows.; The model is verified with analytical solutions for simplified ice jam problems and field data from the Upper Niagara River. The model is also used to study the dynamics of ice jam release.