Stress balances of ice streams in a vertically integrated, higher-order formulation

Abstract

ABSTRACT. One challenge in improving our understanding of ice-stream dynamics is to develop models of the spatial and temporal transition from ice-sheet to ice-stream flow. We address this with a new, vertically integrated, higher-order formulation for ice-sheet dynamics that captures the leading-order physics of low aspect ratio, viscous fluid flow, regardless of the amount of slip at the bed. The theory introduces a parameter, , which approximates the ratio of the basal stress to the shear stress scale, providing a measure of the relative importance of sliding and internal deformation. Our model is able to simultaneously describe the dynamics of both a slow-moving sheet and rapidly flowing ice streams. To test the formulation, we apply a triple-valued sliding law as the basal boundary condition and obtain numerical solutions that can be compared with previous work. We investigate the sensitivity of flow regimes and shear margin width to parameter variation, deriving a scaling for the latter. We also consider a double-valued sliding law, which enforces a constant, low basal stress beneath the ice stream. Comparisons of the resultant stress fields illustrate the different stress balances that can maintain ice-stream flow.

A boundary layer model for ice stream margins

“…Many of these have moved away from coupling leading-order, lubrication-type 'shallow ice' models for ridges to membrane-type 'shallow stream' models across ice stream margins, and employ a hybrid formulation using so-called 'higher-order' models that can be applied regardless of how fast the ice sheet slides (Pattyn 2003;Bueler & Brown 2009;Cornford et al 2013;Kyrke-Smith et al 2013). These are, however, still thin-film models that do not apply in regions where the velocity field changes by O(1) over a single ice thickness (Schoof & Hindmarsh 2010), and therefore cannot be relied on to describe the physics of the stream-ridge boundary layer.…”

“…The relevant jump conditions between ridge and stream models should then be dictated by that boundary layer. The need for a boundary layer persists in principle even for the nowadays widely used 'higher-order' models of ice sheet flow that generalize shearing-and membrane-type flows into a single mathematical description (Pattyn 2003;Kyrke-Smith, Katz & Fowler 2013). Despite their versatility in describing slow shearing flows as well as rapid flows dominated by extensional and lateral stresses, these higher-order models are still only appropriate for thin films (Schoof & Hindmarsh 2010) and cannot accurately capture abrupt transitions between slow and fast flow.…”

The role of basal hydrology in the surging of the Laurentide Ice Sheet

“…Following Le Brocq et al (2009), we model the onset of sliding as a tanh function of water depth, which has been used to simulate sliding at the base of the present-day West Antarctic Ice Sheet. This function takes the form of…”

“…Although water films are generally unstable, ultimately collapsing to a channelised system, in the presence of a sufficiently rough bed they can remain stable (Creyts and Schoof, 2009); furthermore, there is evidence that high water pressure systems exist beneath ice sheets (Engelhardt and Kamb, 1997). The depth of water beneath ice sheets has been argued to be intimately related to the speed with which the overlying ice can slide (Budd and Jenssen, 1987;Le Brocq et al, 2009). Therefore, when considering the onset of sliding during HEs, water must play a very important role.…”

The role of basal hydrology in the surging of the Laurentide Ice Sheet

“…In this study we use the water depth as the switch for the sliding of the ice sheet; therefore, we need to simulate the drainage of water beneath the ice. We model this by assuming that no water drains into the bed beneath the ice sheet; rather, it is forced between the bed and the ice sheet, as if between two parallel plates, by differences in water pressure (Weertman, 1966;Le Brocq et al, 2009). We shall refer to this as the water sheet scheme.…”