Spatiotemporal dynamics of ice streams due to a triple-valued sliding law

Sayag, Roiy; Tziperman, Eli

doi:10.1017/s0022112009991406

Cited by 18 publications

(63 citation statements)

References 69 publications

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“…These are the same three distinct flow regimes that were reported by Sayag and Tziperman (2009), who used the same set-up, but solved the SSA. The regimes illustrated in figures 5-7 in their work directly correspond to those shown in Figure 3 here.…”

Section: Reference Flow Regimes At Smallmentioning

confidence: 70%

“…The details of the derivation are provided in Appendix A. To benchmark the model we consider a set-up based on Sayag and Tziperman (2009) and apply a triple-valued sliding law at the bed. We show our results to be in agreement with theirs.…”

Section: Discussionmentioning

confidence: 99%

“…The ice rheology is taken to be Newtonian, to allow us to compare results with Sayag and Tziperman (2009). Figure 3 shows the three distinct flow regimes that occur as a result of varying the magnitude of the perturbation accumulation, A 0 .…”

Section: Reference Flow Regimes At Smallmentioning

confidence: 99%

“…The first is for zero flow at the bed and the second is with the triple-valued sliding law applied at the bed (as Sayag and Tziperman, 2009). …”

Section: Appendix a Model Derivationmentioning

confidence: 99%

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

Kyrke-Smith¹,

Katz²,

Fowler

2013

J. Glaciol.

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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.

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Section: Reference Flow Regimes At Smallmentioning

confidence: 70%

Section: Discussionmentioning

confidence: 99%

Section: Reference Flow Regimes At Smallmentioning

confidence: 99%

“…The first is for zero flow at the bed and the second is with the triple-valued sliding law applied at the bed (as Sayag and Tziperman, 2009). …”

Section: Appendix a Model Derivationmentioning

confidence: 99%

See 2 more Smart Citations

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

Kyrke-Smith¹,

Katz²,

Fowler

2013

J. Glaciol.

View full text Add to dashboard Cite

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“…This relationship can then be inserted into Eqn (1) to give a multivalued sliding law, where one branch is consistent with surging behaviour (Clarke and others, 1984;Fowler, 1989;Sayag and Tziperman, 2009). If we include the S dependence in the R-channel analysis, the effective pressure in the channels would decrease with increasing S, facilitating the transition to a distributed network for a fixed critical S Λ .…”

Section: Implications For Subglacial Hydrologymentioning

confidence: 99%

Effects of ice deformation on Röthlisberger channels and implications for transitions in subglacial hydrology

et al. 2016

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ABSTRACT. Along the base of glaciers and ice sheets, the sliding of ice over till depends critically on water drainage. In locations where drainage occurs through Röthlisberger channels, the effective pressure along the base of the ice increases and can lead to a strengthening of the bed, which reduces glacier sliding. The formation of Röthlisberger channels depends on two competing effects: (1) melting from turbulent dissipation opens the channel walls and (2) creep flow driven by the weight of the overlying ice closes the channels radially inward. Variation in downstream ice velocity along the channel axis, referred to as an antiplane shear strain rate, decreases the effective viscosity. The softening of the ice increases creep closure velocities. In this way, even a modest addition of antiplane shear can double the size of the Röthlisberger channels for a fixed water pressure or allow channels of a fixed radius to operate at lower effective pressure, potentially decreasing the strength of the surrounding bed. Furthermore, we show that Röthlisberger channels can be deformed away from a circular cross section under applied antiplane shear. These results can have broad impacts on sliding velocities and potentially affect the total ice flux out of glaciers and ice streams.

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Topographically mediated ice stream subglacial drainage networks

2016

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Satellite laser altimetry reveals short timescale changes in Antarctic ice sheet surface elevation that are suggested to be driven by subglacial water transport and storage. Here details of the interaction between the dynamics of ice stream flow, subglacial water system, and bed elevation relief are examined in the context of idealized, heterogeneous bed geometries. Using a two-way coupled model of ice and subglacial water flow, we show that basal topography controls the temporal and spatial variability of the sub-ice stream hydraulic system. The orientation and characteristic dimensions of the topographic undulations determine the morphology (connected subglacial ponds or channel-like subglacial water features) and timescales of the sub-ice stream drainage system. The short-term (several years to decades) variability of the simulated coupled ice stream/subglacial water system suggests that the short-term surface variations detected in remote sensing observations may be indicative of a rapidly evolving subglacial water system. Our simulations also show that interaction between ice flow and the highly dynamic subglacial water system has a strong effect on effective stress in the ice. Large effective stress magnitudes arise over areas where the basal traction is characterized by strong spatial gradients, that is, transitions from high to low basal traction or vise versa. These transitions migrate on multiyear timescales and thus cause large effective stress variability on the same temporal scales.

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Spatiotemporal dynamics of ice streams due to a triple-valued sliding law

Cited by 18 publications

References 69 publications

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

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

Effects of ice deformation on Röthlisberger channels and implications for transitions in subglacial hydrology

Topographically mediated ice stream subglacial drainage networks

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