Abstract

Key Points: 10 • Ice flowing over a rough basal topography may spontaneously develop an inter-11 nal shear band on topographical highs. 12 • The shear strain rate localization and shear heating in the internal shear band is 13 amplified by a non-linear rheology. 14 • We identify two competing mechanisms that affect the energy balance near the 15 bedrock: vertical advective cooling and internal shear heating. Abstract 17 The dramatic acceleration of ice surface speed from upstream to downstream is a no-18 ticeable feature in many ice streams and glaciers. This speed-up is thought to be asso-19 ciated with a transition from internal, distributed deformation to highly localized defor-20 mation at the ice-bedrock interface, but the physical processes governing this transition 21 remain unclear. Here, we argue that basal topography amplifies the feedback between 22 shear heating and localization, leading to the spontaneous formation of an internal shear 23 band for a non-linear rheology. We model the thermo-mechanical ice flow over a simpli-24 fied basal topography using a high-resolution Stokes solver. To capture the interactions 25 between ice and rock, we implement an Immersed Boundary Method and use a level-set 26 approach to represent the free surface of the ice. Our results suggest that an internal shear 27 band can form on topographical highs, continuously heating the basal ice and may grad-28 ually enable a transition to basal sliding. This effect depends sensitively on rheology, with 29 the composite rheology by Goldsby and Kohlstedt (2001) amplifying shear heating no-30 tably. 31 Plain Language Summary 32 On its way towards the ocean, ice speeds up dramatically from less than one me-33 ter per year inland to up to a kilometer per year downstream. In this paper, we inves-34 tigate the physical processes controlling this speed-up. More specifically, we focus on the 35 role that the bedrock topography underneath the ice might play to facilitate this tran-36 sition. We use a two-dimensional numerical model to simulate the temperature distri-37 bution and deformation within a slab of ice flowing down a ramp over a simplified to-38 pography. We find that including basal topography could lead to the development of in-39 ternal shear band located on top of topographical highs. Around half of the total shear 40 deformation within the ice occurs within this band. We compare our model results to 41 borehole measurements from Greenland and find evidence that supports the existence 42 of a shear band. 43