Temperature-dependent shear flow and the absence of thermal runaway in valley glaciers

Abstract

We propose a two-dimensional model of a valley glacier in order to reconsider the question of whether thermal runaway could be a viable mechanism for the onset of creep instability in surging glaciers. We do this by providing an approximate solution for the temperature field based on the idea that shear is concentrated at the glacier bed. With this assumption, we show that a closed-form evolution equation for the glacier profile exists. While this is well known for isoviscous flows, it has not been previously derived for variable viscosity flows. During the process of deriving this equation, we show that thermal runaway does not occur.We provide numerical solutions of the model, and are led to infer that enhanced basal heating owing to refreezing of surface meltwater is an essential constituent in raising the bed temperature to the melting point. © 2009 The Royal Society.