Application of the Saint-Venant model and the modified Stefan model for modeling the formation of the ice cover at the thermal growth stage

Abstract

River ice processes are complex phenomena that are affected by many factors, including meteorological conditions, thermal inputs, hydraulic conditions and channel geometry. Because of the complexity of river ice phenomena and the limited current understanding, the development ofa river ice model requires the maximum use of existing theories and mathematical techniques. In the river hydraulics component, the flow condition is often determined by the solution of the Saint-Venant unsteady flow equations. The complex phenomenon of ice formation at the stage of thermal growth in turn is usually described by models based on the Stefan equation. In current paper we consider the opportunity to use the modified Stefan model, which includes the model of mushy layer in the task of ice thermal grows together with the solution of the problem of Saint-Venant.