Thermal stability properties of a model of glacier flow

We consider the linear stability of the steady state temperature profile in cold regions of valley glaciers. The model we use incorporates surface accumulation and ablation, free surface and melting boundaries and a non‐linear temperature‐dependent viscous flow law. The main simplifying assumption is that the Graetz number is small, in other words the glacier behaves essentially like a slab: although this is not a reasonable assumption, it enables a fully analytic solution of the problem to be obtained, and may point the way for future analyses which include advective heat transport. We find that the steady state is ‘effectively’ stable.