Mathematical Modeling of Rock Glacier Flow with Temperature Effects

This paper stems from the interest in the numerical study of the evolution of Boulder Clay Glacier in Antarctica, whose morphological characteristics have required the revision of the basis for most of the recent mathematical models for glacier dynamics. Bearing in mind the need to minimize the complexity of the mathematical model, we have selected the constitutive equation of rock glacier ice recently presented by two of the authors. Here, this model is extended in order to include temperature effects. In addition to the effects of climate change, it is also necessary to take into consideration the non-negligible level of melting due to temperature changes induced by normal stresses arising from the interactions of ice and the rock fragments that are within the rock glacier. In fact, local phase transition that occurs leading to the release of water implies significant modifications of ice viscosity, the main intrinsic factor driving the flow. In this paper we derive the model that describes the flow of rock glaciers that takes into consideration the effects of temperature and the normal stresses generated by the ice and rock fragments interactions.