A Flow Law for Temperate Glacier Ice

Colbeck, S. C.; Evans, R. J.

doi:10.1017/s0022143000022711

Cited by 80 publications

(50 citation statements)

References 10 publications

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“…Sparse experimental evidence, however, suggests that temperate ice is considerably weaker than cold ice, and that creep may not be modelled reliably according to a standard power law (e.g. Colbeck and Evans, 1973;Duval, 1977;Morgan, 1991). Furthermore, in a basal temperate ice layer it may be that no thermal gradient across an obstacle can be maintained and that pressure melting at the stoss side has different thermal controls than in the classic model.…”

Section: Introductionmentioning

confidence: 99%

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

Krabbendam

2016

The Cryosphere

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Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The classic Weertman model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that pressure melting is limited by heat flow through the obstacle and ductile flow is controlled by standard power-law creep. These last two assumptions, however, are not applicable if a substantial basal layer of temperate (T ∼ T melt ) ice is present. In that case, frictional melting can produce excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. High-temperature ice creep experiments have shown a sharp weakening of a factor 5-10 close to T melt , suggesting standard power-law creep does not operate due to a switch to melt-assisted creep with a possible component of grain boundary melting. Pressure melting is controlled by meltwater production, heat advection by flowing meltwater to the next obstacle and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. Ice streaming over a rough, hard bed, as possibly in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.

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Section: Introductionmentioning

confidence: 99%

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

Krabbendam

2016

The Cryosphere

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“…Meier, 1958Meier, , 1960Lliboutry, 1969;Colbeck and Evans, 1973; 435 Thompson, 1979;Hutter, 1980Hutter, , 1981 …”

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confidence: 99%

The microstructure of polar ice. Part II: State of the art

Faria

Weikusat

Azuma

2014

Journal of Structural Geology

106

189

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Besides the obvious relevance of glaciers and ice sheets for climate-related issues, another important feature of natural ice is its ability to creep on geological time scales and low deviatoric stresses at temperatures very close to its melting point, without losing its polycrystalline character. This fact, together with its strong mechanical anisotropy and other notable properties, makes natural ice an interesting model material for studying the high-temperature creep and recrystallization of rocks in Earth's interior. After having reviewed the major contributions of deep ice coring to the research on natural ice microstructures in Part I of this work (Faria et al., this issue), here in Part II we present an up-to-date view of the modern understanding of natural ice microstructures and the deformation processes that may produce them. In particular, we analyse a large body of evidence that reveals fundamental flaws in the widely accepted tripartite paradigm of polar ice grains is also observed at various depths, provided that the local concentration of strain energy is high enough (which is not seldom the case). As a substitute for the tripartite paradigm, we propose a novel dynamic recrystallization diagram in the three-dimensional state space of strain rate, temperature, and mean grain size, which summarizes the various competing recrystallization processes that contribute to the evolution of the polar ice microstructure.

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“…This parameter, which we will call the finite viscosity parameter σ res , is added to f as: f (σ ) = σ 2 + σ 2 res (see e.g. Colbeck and Evans, 1973). Nonsingular creep functions of non-additive structure have been proposed by e.g.…”

Section: Boundary Layer Treatmentmentioning

confidence: 99%

“…When pushing the asymptotic expansions to second order, the creep response function of the zeroth order effective stress does occur in the denominator. To remedy this, an extra parameter, σ res , is used in Baral (1999) and Baral et al (2001), to regularize the problem, following earlier suggestions by Lliboutry (1969) and Colbeck and Evans (1973). This parameter, which we will call the finite viscosity parameter σ res , is added to f as:…”

Section: J Ahlkrona Et Al: the Second Order Shallow Ice Approximatimentioning

confidence: 99%

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Accuracy of the zeroth- and second-order shallow-ice approximation – numerical and theoretical results

2013

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Abstract. In ice sheet modelling, the shallow-ice approximation (SIA) and second-order shallow-ice approximation (SOSIA) schemes are approaches to approximate the solution of the full Stokes equations governing ice sheet dynamics. This is done by writing the solution to the full Stokes equations as an asymptotic expansion in the aspect ratio , i.e. the quotient between a characteristic height and a characteristic length of the ice sheet. SIA retains the zeroth-order terms and SOSIA the zeroth-, first-, and second-order terms in the expansion. Here, we evaluate the order of accuracy of SIA and SOSIA by numerically solving a two-dimensional model problem for different values of , and comparing the solutions with a finite element solution to the full Stokes equations obtained from Elmer/Ice. The SIA and SOSIA solutions are also derived analytically for the model problem. For decreasing , the computed errors in SIA and SOSIA decrease, but not always in the expected way. Moreover, they depend critically on a parameter introduced to avoid singularities in Glen's flow law in the ice model. This is because the assumptions behind the SIA and SOSIA neglect a thick, high-viscosity boundary layer near the ice surface. The sensitivity to the parameter is explained by the analytical solutions. As a verification of the comparison technique, the SIA and SOSIA solutions for a fluid with Newtonian rheology are compared to the solutions by Elmer/Ice, with results agreeing very well with theory.

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A Flow Law for Temperate Glacier Ice

Cited by 80 publications

References 10 publications

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

The microstructure of polar ice. Part II: State of the art

Accuracy of the zeroth- and second-order shallow-ice approximation – numerical and theoretical results

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