Ice-stream-ice-shelf transition: theoretical analysis of two-dimensional flow

2000 ◽  
Vol 30 ◽  
pp. 153-162 ◽  
Author(s):  
Alexander V. Wilchinsky ◽  
Vladimir A. Chugunov
Keyword(s):  
Shear Stress ◽  
Transition Zone ◽  
Stokes Equations ◽  
Stress Deviator ◽  
Two Dimensional ◽  
Ice Shelf ◽  
Full System ◽  
Ice Stream ◽  
Grounding Line ◽  
Two Dimensional Flow

AbstractTwo-dimensional steady isothermal flow of a marine ice stream is studied. Gases of different relations between shear stress and longitudinal deviatoric stress in the ice stream are considered. Analysis of the ice-stream-ice-shelf transition zone shows that even if the longitudinal stress deviator in the ice stream is much larger than the shear stress (as it is in the ice shelf), the ice-stream-ice-shelf transition zone if singular and the full system of Stokes equations must be solved in it. Scales of fields in the transition zone and the relation between the ice thickness and the horizontal mass flux at the grounding line are found.

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.

scholarly journals A two-dimensional finite-element study of flow in the transition zone between an ice sheet and an ice shelf

1994 ◽  
Vol 20 ◽  
pp. 67-72 ◽  
Author(s):  
Renaud Lestringant
Keyword(s):  
Finite Element ◽  
Transition Zone ◽  
Stokes Equations ◽  
Numerical Study ◽  
Ice Sheet ◽  
Two Dimensional ◽  
Ice Shelf ◽  
Sharp Transition ◽  
Transition Zones ◽  
Dimensional Finite Element

A numerical study has been carried out on the flow of ice in the transition zone between an ice sheet and an ice shelf. The study was motivated by the need for global ice-sheet-ice-shelf modelling to determine the characteristics of the transition zone. The problem is dealt with from an academic viewpoint, and the study especially focuses on two-dimensional vertical sharp transition zones. Stokes equations are solved using a finite-element method. Conclusions include: (1) in ice-sheet-ice-shelf modelling, each of the two components can be computed separately then linked by a jump-boundary condition [or the horizontal velocity; (2) as shown by studies on the response of an ice shelf to tidal forcing, the surface elevation/thickness ratio passes through the hydrostatic equilibrium value.

scholarly journals A two-dimensional finite-element study of flow in the transition zone between an ice sheet and an ice shelf

1994 ◽  
Vol 20 ◽  
pp. 67-72 ◽  
Author(s):  
Renaud Lestringant
Keyword(s):  
Finite Element ◽  
Transition Zone ◽  
Stokes Equations ◽  
Numerical Study ◽  
Ice Sheet ◽  
Two Dimensional ◽  
Ice Shelf ◽  
Sharp Transition ◽  
Transition Zones ◽  
Dimensional Finite Element

A numerical study has been carried out on the flow of ice in the transition zone between an ice sheet and an ice shelf. The study was motivated by the need for global ice-sheet-ice-shelf modelling to determine the characteristics of the transition zone. The problem is dealt with from an academic viewpoint, and the study especially focuses on two-dimensional vertical sharp transition zones. Stokes equations are solved using a finite-element method. Conclusions include: (1) in ice-sheet-ice-shelf modelling, each of the two components can be computed separately then linked by a jump-boundary condition [or the horizontal velocity; (2) as shown by studies on the response of an ice shelf to tidal forcing, the surface elevation/thickness ratio passes through the hydrostatic equilibrium value.

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

The turning couples on an elliptic particle settling in a vertical channel

1994 ◽  
Vol 271 ◽  
pp. 1-16 ◽  
Author(s):  
Peter Y. Huang ◽  
Jimmy Feng ◽  
Daniel D. Joseph
Keyword(s):  
Shear Stress ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Front Face ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Back Face ◽  
The One

We do a direct two-dimensional finite-elment simulation of the Navier–Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes.

scholarly journals Modelling of a marine glacier and ice-sheet-ice-shelf transition zone based on asymptotic analysis

1996 ◽  
Vol 23 ◽  
pp. 59-67 ◽  
Author(s):  
Vladimir A. Chugunov ◽  
Alexander V. Wilchinsky
Keyword(s):  
Boundary Conditions ◽  
Transition Zone ◽  
Spatial Scales ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Stream Length ◽  
Glacier Surface ◽  
Ice Surface ◽  
Grounding Line ◽  
The Difference

All parts of a two-dimensional, isothermal, stationary marine glacier (grounded ice sheet, ice shelf and transition zone) with constant viscosity are analysed by perturbation methods. In so doing, all zones of different flow patterns can be considered separately. Correlations between spatial scales for all parts can be expressed in terms of the typical ice-surface slope distant from the ocean, which reflects exterior conditions of the glacier’s existence. In considering the ice-sheet–ice-shelf transition zone, a small parameter characterizing the difference between ice and water densities is used. Such an analysis allows us to find boundary conditions at the grounding line for the grounded ice mass. Glacier-surface profiles are determined by numerical methods. The grounding-line position found by using the boundary conditions derived in this paper differs from that obtained by using Thomas and Bentley’s (1978) boundary conditions by about 10% of the grounded ice-stream length.

scholarly journals Ice-shelf Response to Ice-stream Discharge Fluctuations: I. Unconfined Ice Tongues

1988 ◽  
Vol 34 (116) ◽  
pp. 121-127 ◽  
Author(s):  
Douglas R. MacAyeal ◽  
Victor Barcilon
Keyword(s):  
Ice Shelf ◽  
Lagrangian Particle ◽  
Sea Level Fluctuations ◽  
Stream Discharge ◽  
Discharge Fluctuations ◽  
Ice Stream ◽  
Grounding Line ◽  
Velocity Changes ◽  
Particle Paths

AbstractIce-stream discharge fluctuations constitute an independent means of forcing unsteady ice-shelf behavior, and their effect must be distinguished from those of oceanic and atmospheric climate to understand ice-shelf change. In addition, ice-stream-generated thickness anomalies may constitute a primary trigger of ice-rise formation in the absence of major sea-level fluctuations. Such triggering may maintain the current ice-rise population that, in turn, contributes to long-term ice-sheet stability. Here, we show that ice-stream-generated fluctuations of an ideal, two-dimensional ice shelf propagate along two characteristic trajectories. One trajectory permits instantaneous transmission of grounding-line velocity changes to all points down-stream. The other trajectory represents slow transmission of grounding-line thickness changes along Lagrangian particle paths.

scholarly journals Ice-shelf Response to Ice-stream Discharge Fluctuations: I. Unconfined Ice Tongues

1988 ◽  
Vol 34 (116) ◽  
pp. 121-127 ◽  
Author(s):  
Douglas R. MacAyeal ◽  
Victor Barcilon
Keyword(s):  
Ice Shelf ◽  
Lagrangian Particle ◽  
Sea Level Fluctuations ◽  
Stream Discharge ◽  
Discharge Fluctuations ◽  
Ice Stream ◽  
Grounding Line ◽  
Velocity Changes ◽  
Particle Paths

AbstractIce-stream discharge fluctuations constitute an independent means of forcing unsteady ice-shelf behavior, and their effect must be distinguished from those of oceanic and atmospheric climate to understand ice-shelf change. In addition, ice-stream-generated thickness anomalies may constitute a primary trigger of ice-rise formation in the absence of major sea-level fluctuations. Such triggering may maintain the current ice-rise population that, in turn, contributes to long-term ice-sheet stability. Here, we show that ice-stream-generated fluctuations of an ideal, two-dimensional ice shelf propagate along two characteristic trajectories. One trajectory permits instantaneous transmission of grounding-line velocity changes to all points down-stream. The other trajectory represents slow transmission of grounding-line thickness changes along Lagrangian particle paths.

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