An anisotropic flow law for ice-sheet ice and its implications

A new flow law for anisotropic polycrystalline ice is presented. The strain-rate tensor is related by a geometrical factor tensor (G) to the stress tensor. The G factor tensor can be obtained front the c-axis fabric data and stress condition. This new flow law describes well the direction-dependent mechanical properties of anisotropic ice which cannot be demonstrated by Glen’s flow law. For example, the new flow law can explain the fact that a strong single-maximum fabric ice, such as Dye 3 Wisconsin ice, can deform several times faster than isotropic ice under horizontal shear but can hardly deform under vertical or horizontal normal stress. We also show that at a deeper part of an ice sheet, where a single-maximum fabric develops, a positive vertical strain rate can be produced with only a horizontal shear stress.

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Fabric Analysis of Surface Ice near Casey Range, East Antarctica

Journal of Glaciology ◽

10.1017/s0022143000026964 ◽

1969 ◽

Vol 8 (54) ◽

pp. 375-383 ◽

Cited By ~ 6

Author(s):

Koshiro Kizaki

Keyword(s):

Strain Rate ◽

Grain Growth ◽

Ice Sheet ◽

East Antarctica ◽

Ice Streams ◽

Antarctic Ice Sheet ◽

Single Maximum ◽

Fabric Analysis ◽

Surface Ice ◽

The Antarctic

AbstractForbes Glacier, one of the outlet ice streams from the Antarctic ice sheet, is located 20 km west of Mawson, Mac.Robertson Land, east Antarctica. In the uppermost part of the glacier near Casey Range, the velocity at the centre of the glacier is 59 m year−1and the strain-rate at seven strain grids ranges from −6.7 to 6.7×10−3year−1on the surface of the glacier. The fabric types of this area are characterized by single-maximum and small-girdle fabrics. It is confirmed that the single-maximum fabric is an original pattern which changes gradually to a small girdle fabric about the maximum compressive axis in association with grain growth. The patterns predicted by Brace (1960) can be adapted to the small-girdle fabrics of this area.

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The effect of anisotropic flow properties on ice-sheet surface elevation change

Annals of Glaciology ◽

10.3189/172756404781813989 ◽

2004 ◽

Vol 39 ◽

pp. 439-444 ◽

Cited By ~ 1

Author(s):

Weili Wang ◽

Jun Li ◽

Jay Zwally ◽

Vin Morgan ◽

Tas D. Van Ommen

Keyword(s):

Strain Rate ◽

Ice Sheet ◽

Surface Elevation ◽

Ice Thickness ◽

Flow Properties ◽

Elevation Change ◽

Ice Flow ◽

Anisotropic Flow ◽

Sheet Surface ◽

Surface Elevation Change

AbstractAn ice-flow model has been developed and applied to Law Dome, East Antarctica, at the location of the Dome Summit South deep borehole. The results are used to reconstruct an ice-sheet history of accumulation rate, ice thickness and the rate of change in ice thickness. The focus of this study is on the effect of the variation in anisotropic flow properties on the ice-sheet surface elevation change. The enhancement factor, defined as the ratio of the strain rate for anisotropic ice to the strain rate for isotropic ice, is used in the ice-flow relations to account for the anisotropic properties of the ice with fabric development. The model is run with the various ice rheologies which represent anisotropic or isotropic ice-flow properties. The results show that the model incorporating anisotropic flow properties of the ice is more sensitive to the climate-change history.

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Structure and Flow in the Margin of the Barnes Ice Cap, Baffin Island, N.W.T., Canada

Journal of Glaciology ◽

10.1017/s0022143000031841 ◽

1973 ◽

Vol 12 (66) ◽

pp. 423-438 ◽

Cited By ~ 77

Author(s):

Roger Leb. Hooke

Keyword(s):

Flow Field ◽

Strain Rate ◽

Effective Strain ◽

The Other ◽

Baffin Island ◽

Glacier Surface ◽

Effective Strain Rate ◽

Ice Cap ◽

Single Maximum ◽

Flow Law

The structure and flow field in the margin of the Barnes Ice Cap was determined through observations on the ice-cap surface, in four bore holes, and in a 125 m ice tunnel. A band of fine bubbly white ice with a single maximum fabric appears at the glacier surface about 160 m from the margin. This band is overlain by coarse blue ice with a four-maximum fabric, and underlain by alternating bands of fine ice with a single-maximum fabric and moderately coarse ice with a two or three-maximum fabric. The effective strain rate was determined from the bore-hole and tunnel deformation data, and possible variations in the other three parameters in Glen’s flow law, , were studied. It appears that τ xy is independent of depth near the surface, and that relative to the coarse blue ice, A is 40 to 50% lower in the white ice and possibly 10% lower in the fine blue ice. Dips of foliation planes decrease rapidly with increasing depth and distance from the margin. This foliation is assumed to have developed near and parallel to the bed some distance from the margin. An analysis based on this assumption predicts the observed change in dip, but suggests that it did not develop under the present flow field. The ice cap was probably thicker a few tens of years ago, and the observed foliation pattern may be a relict from that time.

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Structure and Flow in the Margin of the Barnes Ice Cap, Baffin Island, N.W.T., Canada

Journal of Glaciology ◽

10.3189/s0022143000031841 ◽

1973 ◽

Vol 12 (66) ◽

pp. 423-438 ◽

Cited By ~ 2

Author(s):

Roger Leb. Hooke

Keyword(s):

Flow Field ◽

Strain Rate ◽

Effective Strain ◽

The Other ◽

Baffin Island ◽

Glacier Surface ◽

Effective Strain Rate ◽

Ice Cap ◽

Single Maximum ◽

Flow Law

The structure and flow field in the margin of the Barnes Ice Cap was determined through observations on the ice-cap surface, in four bore holes, and in a 125 m ice tunnel. A band of fine bubbly white ice with a single maximum fabric appears at the glacier surface about 160 m from the margin. This band is overlain by coarse blue ice with a four-maximum fabric, and underlain by alternating bands of fine ice with a single-maximum fabric and moderately coarse ice with a two or three-maximum fabric.The effective strain rate was determined from the bore-hole and tunnel deformation data, and possible variations in the other three parameters in Glen’s flow law, , were studied. It appears that τxy is independent of depth near the surface, and that relative to the coarse blue ice, A is 40 to 50% lower in the white ice and possibly 10% lower in the fine blue ice.Dips of foliation planes decrease rapidly with increasing depth and distance from the margin. This foliation is assumed to have developed near and parallel to the bed some distance from the margin. An analysis based on this assumption predicts the observed change in dip, but suggests that it did not develop under the present flow field. The ice cap was probably thicker a few tens of years ago, and the observed foliation pattern may be a relict from that time.

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Fabric Analysis of Surface Ice near Casey Range, East Antarctica

Journal of Glaciology ◽

10.3189/s0022143000026964 ◽

1969 ◽

Vol 8 (54) ◽

pp. 375-383

Author(s):

Koshiro Kizaki

Keyword(s):

Strain Rate ◽

Grain Growth ◽

Ice Sheet ◽

East Antarctica ◽

Ice Streams ◽

Antarctic Ice Sheet ◽

Single Maximum ◽

Fabric Analysis ◽

Surface Ice ◽

The Antarctic

AbstractForbes Glacier, one of the outlet ice streams from the Antarctic ice sheet, is located 20 km west of Mawson, Mac.Robertson Land, east Antarctica. In the uppermost part of the glacier near Casey Range, the velocity at the centre of the glacier is 59 m year−1 and the strain-rate at seven strain grids ranges from −6.7 to 6.7×10−3 year−1 on the surface of the glacier. The fabric types of this area are characterized by single-maximum and small-girdle fabrics. It is confirmed that the single-maximum fabric is an original pattern which changes gradually to a small girdle fabric about the maximum compressive axis in association with grain growth. The patterns predicted by Brace (1960) can be adapted to the small-girdle fabrics of this area.

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A topological approach to the strain-rate pattern of ice sheets

Journal of Glaciology ◽

10.3189/s0022143000015677 ◽

1993 ◽

Vol 39 (131) ◽

pp. 10-14 ◽

Cited By ~ 1

Author(s):

J. F. Nye

Keyword(s):

Strain Rate ◽

Ice Sheets ◽

Ice Sheet ◽

Point Of View ◽

Principal Strain ◽

Topological Approach ◽

Contour Maps ◽

Isotropic Point ◽

Horizontal Strain

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

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Strain-Rate and Grain‒Size Effects in Ice

Journal of Glaciology ◽

10.1017/s0022143000008844 ◽

1987 ◽

Vol 33 (115) ◽

pp. 274-280 ◽

Cited By ~ 50

Author(s):

David M. Cole

Keyword(s):

Grain Size ◽

Strain Rate ◽

Transition Point ◽

Boundary Migration ◽

Peak Stress ◽

Strain Rates ◽

Thin Sections ◽

Fine Grained ◽

Lower Strain ◽

Polycrystalline Ice

AbstractThis paper presents and discusses the results of constant deformation-rate tests on laboratory-prepared polycrystalline ice. Strain-rates ranged from 10−7to 10−1s−1, grain–size ranged from 1.5 to 5.8 mm, and the test temperature was −5°C.At strain-rates between 10−7and 10−3s−1, the stress-strain-rate relationship followed a power law with an exponent ofn= 4.3 calculated without regard to grain-size. However, a reversal in the grain-size effect was observed: below a transition point near 4 × 10−6s−1the peak stress increased with increasing grain-size, while above the transition point the peak stress decreased with increasing grain-size. This latter trend persisted to the highest strain-rates observed. At strain-rates above 10−3s−1the peak stress became independent of strain-rate.The unusual trends exhibited at the lower strain-rates are attributed to the influence of the grain-size on the balance of the operative deformation mechanisms. Dynamic recrystallization appears to intervene in the case of the finer-grained material and serves to lower the peak stress. At comparable strain-rates, however, the large-grained material still experiences internal micro-fracturing, and thin sections reveal extensive deformation in the grain-boundary regions that is quite unlike the appearance of the strain-induced boundary migration characteristic of the fine-grained material.

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Contribution to the Movement and the form of Ice Sheets in the Arctic and Antarctic

Journal of Glaciology ◽

10.3189/s0022143000017548 ◽

1961 ◽

Vol 3 (30) ◽

pp. 1133-1151 ◽

Cited By ~ 4

Author(s):

R. Haefeli

Keyword(s):

Average Rate ◽

Ice Sheet ◽

Surface Profile ◽

Greenland Ice Sheet ◽

Present Theory ◽

The Arctic ◽

Small Influence ◽

Horizontal Velocity Component ◽

Flow Law ◽

Set Up

AbstractStarting from Glen’s flow law for ice and from a series of assumptions based in part on observations in Greenland and in the Jungfraujoch, the velocity distribution (horizontal velocity component) and surface configuration is derived for a strip-shaped ice sheet in a stationary state. For the choice n = 3 − 4 of the exponent in the power-law flow relation, there is extensive agreement between the theoretically calculated surface profile and the east-west profile measured through “Station Centrale” by Expéditions Polaires Françaises. The corresponding theoretical solution for a circular ice sheet is also given. As a first application of this theory, an attempt is made to calculate the average rate of accumulation in Antarctica from its surface profile (assumed circular in plan) and from the flow-law parameters derived from the Greenland Ice Sheet. It is also shown that a change in accumulation has only a small influence on the total ice thickness of an ice sheet. A method of calculating approximately the age of ice in an ice sheet, based on the foregoing theory, is illustrated by applying it to the Greenland Ice Sheet. After comparing the present theory with that of Nye, a general expression for the surface profile of an ice sheet with constant accumulation is set up and discussed by means of comparison with two profiles through Antarctica.

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LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

Volume 2C: Turbomachinery ◽

10.1115/gt2018-75792 ◽

2018 ◽

Author(s):

Jean-François Monier ◽

Nicolas Poujol ◽

Mathieu Laurent ◽

Feng Gao ◽

Jérôme Boudet ◽

...

Keyword(s):

Strain Rate ◽

Stress Tensor ◽

Reynolds Stress ◽

Constitutive Relation ◽

Strain Rate Tensor ◽

Separation Flow ◽

Compressor Cascade ◽

Corner Separation ◽

Reynolds Stress Tensor ◽

Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

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