Double Layer–Averaged Model of River Ice–Water Mixture Flow

Abstract

River ice–water mixture flows are commonly occurring natural phenomena that have the potential to cause serious hazards. To date, however, the interactive processes between ice and water have remained poorly understood. Existing mathematical models of river ice–water mixture flows are physically simplified because they do not fully account for the effect of ice. Here, a double layer–averaged model is proposed to facilitate a refined simulation of river ice–water mixture flows, which are often characterized by a vertical double-layer structure composed of an upper ice–water mixture flow layer and a lower clear-water flow layer immediately above the riverbed. Two hyperbolic systems of governing equations for the two layers are derived from mass and momentum conservation laws and numerically solved separately (and synchronously) using a finite-volume slope limited centered scheme. Interlayer interactions are negligible compared with inertia and gravity effects. Hence, the model achieves a satisfactory balance between flux gradients and bed and interface slope source terms, and so is applicable to ice–water flows over irregular topography. The model is first benchmarked against a hypothetical ice jam release event and then applied to an actual ice jam release event that occurred in the Athabasca River, Canada, in 2002. It is demonstrated that the model satisfactorily resolves the processes driving river ice–water mixture flows. The paper presents a promising future framework for river ice–water mixture flow modeling by practitioners.