scholarly journals The Effect of Longitudinal Strain on the Shear Stress of an Ice Sheet: In Defence of Using Stretched Coordinates

1981 ◽  
Vol 27 (95) ◽  
pp. 39-56 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Shear Stress ◽  
Longitudinal Strain ◽  
Ice Sheets ◽  
Governing Equations ◽  
Classical Formula ◽  
Straightforward Manner ◽  
Vertical Variations ◽  
Smallness Parameter ◽  
Basal Shear ◽  
Surface Changes

AbstractThickness changes of ice sheets are, except perhaps at the snout region, small as compared to unity. This suggests using a coordinate stretching so as to make the surface changes in the new coordinates of order one. The explicit occurrence of the smallness parameter in the governing equations then allows us to search for perturbation solutions in various problems. Here, it is shown that the classical formula for the basal shear stress follows easily from such a perturbation procedure. Furthermore it can be improved to account for longitudinal strain effects. As compared to previous work in this area, these formulae are explicit and allow us to take vertical variations of material properties into account in a straightforward manner.

The Effect of Longitudinal Strain on the Shear Stress of an Ice Sheet: In Defence of Using Stretched Coordinates

1981 ◽  
Vol 27 (95) ◽  
pp. 39-56 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Shear Stress ◽  
Longitudinal Strain ◽  
Ice Sheets ◽  
Governing Equations ◽  
Classical Formula ◽  
Straightforward Manner ◽  
Vertical Variations ◽  
Smallness Parameter ◽  
Basal Shear ◽  
Surface Changes

Abstract Thickness changes of ice sheets are, except perhaps at the snout region, small as compared to unity. This suggests using a coordinate stretching so as to make the surface changes in the new coordinates of order one. The explicit occurrence of the smallness parameter in the governing equations then allows us to search for perturbation solutions in various problems. Here, it is shown that the classical formula for the basal shear stress follows easily from such a perturbation procedure. Furthermore it can be improved to account for longitudinal strain effects. As compared to previous work in this area, these formulae are explicit and allow us to take vertical variations of material properties into account in a straightforward manner.

scholarly journals The Effect of Longitudinal Stress on the Shear Stress at the Base of an Ice Sheet

1969 ◽  
Vol 8 (53) ◽  
pp. 207-213 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Shear Stress ◽  
Theoretical Basis ◽  
Ice Sheets ◽  
Ice Sheet ◽  
High Accuracy ◽  
Longitudinal Stress ◽  
Surface Slope ◽  
Two Dimensional Flow ◽  
Basal Shear ◽  
Longitudinal Strain Rate

Robin (1967) and Budd (1968, unpublished) have succeeded in connecting the variations in surface slope of an ice sheet with variations in the gradient of the longitudinal strain-rate. This paper tries to improve the theoretical basis of their work. By choice of a suitable coordinate system and suitable redefinition of the variables, Budd’s formula for the basal shear stress is derived with a minimum of restrictive assumptions. The resulting formula, containing the gradient of a longitudinal stress, is thought to be of high accuracy for the two-dimensional flow of cold ice sheets, and is valid for slopes of any magnitude.

scholarly journals Ribbed bedforms on palaeo-ice stream beds resemble regular patterns of basal shear stress (‘traction ribs’) inferred from modern ice streams

2016 ◽  
Vol 62 (234) ◽  
pp. 696-713 ◽  
Author(s):  
CHRIS R. STOKES ◽  
MARTIN MARGOLD ◽  
TIMOTHY T. CREYTS
Keyword(s):  
Shear Stress ◽  
Ice Sheets ◽  
Western Canada ◽  
Coupled Flow ◽  
Ice Streams ◽  
Ice Stream ◽  
Stream Beds ◽  
Basal Shear ◽  
Subglacial Meltwater ◽  
Regular Patterns

Rapidly-flowing ice streams are an important mechanism through which ice sheets lose mass, and much work has been focussed on elucidating the processes that increase or decrease their velocity. Recent work using standard inverse methods has inferred previously-unrecognised regular patterns of high basal shear stress (‘sticky spots’ >200 kPa) beneath a number of ice streams in Antarctica and Greenland, termed ‘traction ribs’. They appear at a scale intermediate between smaller ribbed moraines and much larger mega-ribs observed on palaeo-ice sheet beds, but it is unclear whether they have a topographic expression at the bed. Here, we report observations of rib-like bedforms from DEMs along palaeo-ice stream beds in western Canada that resemble both the pattern and dimensions of traction ribs. Their identification suggests that traction ribs may have a topographic expression that lies between, and partly overlaps with, ribbed moraines and much larger mega-ribs. These intermediate-sized bedforms support the notion of a ribbed bedform continuum. Their formation remains conjectural, but our observations from palaeo-ice streams, coupled with those from modern ice masses, suggest they are related to wave-like instabilities occurring in the coupled flow of ice and till and modulated by subglacial meltwater drainage. Their form and pattern may also involve glaciotectonism of subglacial sediments.

scholarly journals Glacier hydromechanics: early insights and the lasting legacy of three works by Iken and colleagues

2010 ◽  
Vol 56 (200) ◽  
pp. 1069-1078 ◽  
Author(s):  
Gwenn E. Flowers
Keyword(s):  
Shear Stress ◽  
Vertical Velocity ◽  
Water Pressure ◽  
Ice Sheets ◽  
Strong Correlations ◽  
Velocity Measurements ◽  
Short Term ◽  
Ice Flow ◽  
Alpine Glaciers ◽  
Basal Shear

AbstractThe association between basal hydrology and glacier sliding has become nearly synonymous with the early work of Almut Iken and colleagues. Their research published in theJournal of Glaciologyfrom 1981 to 1986 made an indelible impact on the study of glacier hydromechanics by documenting strong correlations between basal water pressure and short-term ice-flow variations. With a passion for elucidating the physics of glacier-bed processes, Iken herself made fundamental contributions to our theoretical and empirical understanding of the sliding process. From the theoretical bound on basal shear stress, to the inferences drawn from detailed horizontal and vertical velocity measurements, the work of Iken and colleagues continues to inform the interpretation of data from alpine glaciers and has found increasing relevance to observations from the ice sheets.

scholarly journals The Sliding Velocity of Athabasca Glacier, Canada

1970 ◽  
Vol 9 (55) ◽  
pp. 55-63 ◽  
Author(s):  
W. S. B. Paterson
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Shear Stresses ◽  
Sliding Velocity ◽  
Flow Law ◽  
Basal Shear ◽  
Longitudinal Strain Rate

AbstractA method of estimating siding velocity is presented. It rests on few assumptions, one of which is that longitudinal strain-rate varies linearly with depth. The flow law of ice is not used. To apply it, the sliding velocity at one point must be known. The method is used to calculate the sliding velocity at twelve points on Athabasca Glacier. These values are not related to calculated basal shear stresses. Thus one or more of the following statements must be true: (1) basal shear stress cannot be calculated by the conventional formula, (2) the roughness of the glacier bed varies from place to place, (3) sliding velocity does not obey Weertman's formula. Analysis of seven published measurements of sliding velocity leads to the same conclusion.

scholarly journals Reconstruction and Disintegration of Ice Sheets for the Climap 18000 and 125000 Years B.P. Experiments: Theory

1979 ◽  
Vol 24 (90) ◽  
pp. 493-495
Author(s):  
T. J. Hughes
Keyword(s):  
Shear Stress ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Frictional Heat ◽  
Ice Streams ◽  
Ice Stream ◽  
Grounding Line ◽  
Flow Law ◽  
Basal Shear ◽  
Stress Variations

AbstractSize, shape, and surface albedo of former ice sheets are needed in order to model atmospheric circulation for the CLIMAP 18000 years B.P. experiment. Both the size and shape of an ice sheet depend on the hardness of ice and its coupling to bedrock. Ice hardness is controlled by ice temperature and fabric, which are not adequately described by any ice flow law. Ice–bed coupling is controlled by bed roughness and basal melt water, which are not adequately described by any ice sliding law. With these inadequacies in mind, we assumed equilibrium ice-sheet conditions 18000 years ago and combined the standard steady-state flow and sliding laws of ice with the equation of mass balance to obtain separate basal shear-stress variations along ice-sheet flow lines for a frozen bed when the flow law dominates and for a melted bed when the sliding law dominates. Theoretical basal shear-stress variations were then derived for freezing and melting beds on the assumption that separate melted areas of the bed had water films of constant thickness which expanded and merged for a melting bed but contracted and separated for a freezing bed. Theoretical basal shear-stress variations were also derived for ice streams along marine ice-sheet margins and ice lobes along terrestrial ice-sheet margins on the assumption that the entire area of their bed was wet so that further melting increased the water-layer thickness, which would then be decreased by freezing. Melting was assumed to continue to the grounding line of an ice stream and the minimum-slope surface inflection line of an ice lobe, where freezing began and continued to the ice-lobe terminus. Ice–bed uncoupling is complete at an ice-stream grounding line and maximized at an ice-lobe minimum-slope inflection line, so ice velocity and consequent generation of frictional heat were assumed to reach maxima across these lines. Theoretical basal shear-stress variations were derived for the zone of converging flow at the heads of ice streams and ice lobes, and from domes to saddles along the ice divide for both frozen and melted beds.

scholarly journals Reconstruction and Disintegration of Ice Sheets for the Climap 18000 and 125000 Years B.P. Experiments: Theory

1979 ◽  
Vol 24 (90) ◽  
pp. 493-495 ◽  
Author(s):  
T. J. Hughes
Keyword(s):  
Shear Stress ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Frictional Heat ◽  
Ice Streams ◽  
Ice Stream ◽  
Grounding Line ◽  
Flow Law ◽  
Basal Shear ◽  
Stress Variations

Abstract Size, shape, and surface albedo of former ice sheets are needed in order to model atmospheric circulation for the CLIMAP 18000 years B.P. experiment. Both the size and shape of an ice sheet depend on the hardness of ice and its coupling to bedrock. Ice hardness is controlled by ice temperature and fabric, which are not adequately described by any ice flow law. Ice–bed coupling is controlled by bed roughness and basal melt water, which are not adequately described by any ice sliding law. With these inadequacies in mind, we assumed equilibrium ice-sheet conditions 18000 years ago and combined the standard steady-state flow and sliding laws of ice with the equation of mass balance to obtain separate basal shear-stress variations along ice-sheet flow lines for a frozen bed when the flow law dominates and for a melted bed when the sliding law dominates. Theoretical basal shear-stress variations were then derived for freezing and melting beds on the assumption that separate melted areas of the bed had water films of constant thickness which expanded and merged for a melting bed but contracted and separated for a freezing bed. Theoretical basal shear-stress variations were also derived for ice streams along marine ice-sheet margins and ice lobes along terrestrial ice-sheet margins on the assumption that the entire area of their bed was wet so that further melting increased the water-layer thickness, which would then be decreased by freezing. Melting was assumed to continue to the grounding line of an ice stream and the minimum-slope surface inflection line of an ice lobe, where freezing began and continued to the ice-lobe terminus. Ice–bed uncoupling is complete at an ice-stream grounding line and maximized at an ice-lobe minimum-slope inflection line, so ice velocity and consequent generation of frictional heat were assumed to reach maxima across these lines. Theoretical basal shear-stress variations were derived for the zone of converging flow at the heads of ice streams and ice lobes, and from domes to saddles along the ice divide for both frozen and melted beds.

scholarly journals The Effect of Longitudinal Stress on the Shear Stress at the Base of an Ice Sheet

1969 ◽  
Vol 8 (53) ◽  
pp. 207-213 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Shear Stress ◽  
Theoretical Basis ◽  
Ice Sheets ◽  
Ice Sheet ◽  
High Accuracy ◽  
Longitudinal Stress ◽  
Surface Slope ◽  
Two Dimensional Flow ◽  
Basal Shear ◽  
Longitudinal Strain Rate

Robin (1967) and Budd (1968, unpublished) have succeeded in connecting the variations in surface slope of an ice sheet with variations in the gradient of the longitudinal strain-rate. This paper tries to improve the theoretical basis of their work. By choice of a suitable coordinate system and suitable redefinition of the variables, Budd’s formula for the basal shear stress is derived with a minimum of restrictive assumptions. The resulting formula, containing the gradient of a longitudinal stress, is thought to be of high accuracy for the two-dimensional flow of cold ice sheets, and is valid for slopes of any magnitude.

scholarly journals The Sliding Velocity of Athabasca Glacier, Canada

1970 ◽  
Vol 9 (55) ◽  
pp. 55-63
Author(s):  
W. S. B. Paterson
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Shear Stresses ◽  
Sliding Velocity ◽  
Flow Law ◽  
Basal Shear ◽  
Longitudinal Strain Rate

AbstractA method of estimating siding velocity is presented. It rests on few assumptions, one of which is that longitudinal strain-rate varies linearly with depth. The flow law of ice is not used. To apply it, the sliding velocity at one point must be known. The method is used to calculate the sliding velocity at twelve points on Athabasca Glacier. These values are not related to calculated basal shear stresses. Thus one or more of the following statements must be true: (1) basal shear stress cannot be calculated by the conventional formula, (2) the roughness of the glacier bed varies from place to place, (3) sliding velocity does not obey Weertman's formula. Analysis of seven published measurements of sliding velocity leads to the same conclusion.

scholarly journals Sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions: a model study

2002 ◽  
Vol 48 (163) ◽  
pp. 552-558 ◽  
Author(s):  
Marjorie Schmeltz ◽  
Eric Rignot ◽  
Todd K. Dupont ◽  
Douglas R. MacAyeal
Keyword(s):  
Shear Stress ◽  
Element Model ◽  
Shelf Area ◽  
West Antarctica ◽  
Ice Shelf ◽  
Ice Stream ◽  
Model Study ◽  
Grounding Line ◽  
Glacier Velocity ◽  
Basal Shear

AbstractWe use a finite-element model of coupled ice-stream/ice-shelf flow to study the sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions. By tuning a softening coefficient of the ice along the glacier margins, and a basal friction coefficient controlling the distribution of basal shear stress underneath the ice stream, we are able to match model velocity to that observed with interferometric synthetic aperture radar (InSAR). We use the model to investigate the effect of small perturbations on ice flow. We find that a 5.5–13% reduction in our initial ice-shelf area increases the glacier velocity by 3.5–10% at the grounding line. The removal of the entire ice shelf increases the grounding-line velocity by > 70%. The changes in velocity associated with ice-shelf reduction are felt several tens of km inland. Alternatively, a 5% reduction in basal shear stress increases the glacier velocity by 13% at the grounding line. By contrast, softening of the glacier side margins would have to be increased a lot more to produce a comparable change in ice velocity. Hence, both the ice-shelf buttressing and the basal shear stress contribute significant resistance to the flow of Pine Island Glacier.

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