scholarly journals Surface Contours and Flow Pattern of a Perfectly Plastic Three-Dimensional Ice Sheet With Arbitrary Bottom and Edge Topography

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh

Abstract The differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.


1982 ◽  
Vol 28 (100) ◽  
pp. 431-455 ◽  
Author(s):  
Niels Reeh

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple case, (1) an ice sheet on a horizontal base with an arbitrary edge curve, and (2) an ice sheet on a plane sloping base with a rectilinear ice margin. The solutions are discussed, particularly with reference to the development of ice divides and ice streams.For arbitrary base and ice-margin geometries, solutions are obtained by means of the method of characteristics, which reduces the problem to solving simultaneously three ordinary first-order differential equations. The integration, which is performed by numerical methods, is generally commenced at the ice margin, where the necessary boundary conditions are known.The method has been applied to model the elevation contours and the flow pattern of the central Greenland ice sheet, using the bottom topography revealed by radio echo soundings and the present ice margin geometry. The result is in surprisingly good agreement with our knowledge of the ice-sheet topography and flow pattern, all significant ice divides and ice streams being reproduced. This suggests, that the method can be applied to model the shape and flow pattern of ice sheets under glacial conditions, using information about former ice-margin positions.


1982 ◽  
Vol 28 (100) ◽  
pp. 431-455 ◽  
Author(s):  
Niels Reeh

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple case, (1) an ice sheet on a horizontal base with an arbitrary edge curve, and (2) an ice sheet on a plane sloping base with a rectilinear ice margin. The solutions are discussed, particularly with reference to the development of ice divides and ice streams.For arbitrary base and ice-margin geometries, solutions are obtained by means of the method of characteristics, which reduces the problem to solving simultaneously three ordinary first-order differential equations. The integration, which is performed by numerical methods, is generally commenced at the ice margin, where the necessary boundary conditions are known.The method has been applied to model the elevation contours and the flow pattern of the central Greenland ice sheet, using the bottom topography revealed by radio echo soundings and the present ice margin geometry. The result is in surprisingly good agreement with our knowledge of the ice-sheet topography and flow pattern, all significant ice divides and ice streams being reproduced. This suggests, that the method can be applied to model the shape and flow pattern of ice sheets under glacial conditions, using information about former ice-margin positions.


1999 ◽  
Vol 28 ◽  
pp. 83-89 ◽  
Author(s):  
A. J. Payne ◽  
D.J. Baldwin

AbstractThis work attempts to explain the fan-like landform assemblages observed in satellite images of the area covered by the former Scandinavian ice sheet (SIS). These assemblages have been interpreted as evidence of large ice streams within the SIS. If this interpretation is correct, then it calls into doubt current theories on the formation of ice streams. These theories regard soft sediment and topographic troughs as being the key determinants of ice-stream location. Neither can be used to explain the existence of ice streams on the flat, hard-rock area of the Baltic Shield. Initial results from a three-dimensional, thermomechanical ice-sheet model indicate that interactions between ice flow, form and temperature can create patterns similar to those mentioned above. The model uses a realistic, 20 km resolution gridded topography and a simple parameterization of accumulation and ablation. It produces patterns of maximum ice-sheet extent, which are similar to those reconstructed from the area’s glacial geomorphology. Flow in the maximum, equilibrium ice sheet is dominated by wedges of warm, low-viscosity, fast-flowing ice. These are separated by areas of cold, slow-flowing ice. This patterning appears to develop spontaneously as the modelled ice sheet grows.


2007 ◽  
Vol 39 (3) ◽  
pp. 229-238 ◽  
Author(s):  
D. A. Fisher ◽  
N. Reeh ◽  
K. Langley

ABSTRACT A three dimensional steady state plastic ice model; the present surface topography (on a 50 km grid); a recent concensus of the Late Wisconsinan maximum margin (PREST, 1984); and a simple map of ice yield stress are used to model the Laurentide Ice Sheet. A multi-domed, asymmetric reconstruction is computed without prior assumptions about flow lines. The effects of possible deforming beds are modelled by using the very low yield stress values suggested by MATHEWS (1974). Because of low yield stress (deforming beds) the model generates thin ice on the Prairies, Great Lakes area and, in one case, over Hudson Bay. Introduction of low yield stress (deformabie) regions also produces low surface slopes and abrupt ice flow direction changes. In certain circumstances large ice streams are generated along the boundaries between normal yield stress (non-deformable beds) and low yield stress ice (deformabie beds). Computer models are discussed in reference to the geologically-based reconstructions of SHILTS (1980) and DYKE ef al. (1982).


1984 ◽  
Vol 5 ◽  
pp. 115-121 ◽  
Author(s):  
N. Reeh

A three-dimensional perfectly plastic ice-sheet model, developed for determining the surface elevations and the flow pattern of an ice sheet with given bottom topography and ice-margin positions, is applied to the reconstruction of the glacial ice covers of Greenland and the Canadian Arctic islands. In the northern regions, two different reconstructions have been performed with ice margins along the present 600 and 200 m sea-depth contours, respectively. In central Greenland, the ice margin is considered to be at the outermost ice-margin deposits on the coastal shelf to the west, and at the present 200 m sea-depth contour to the east.The main conclusions to be drawn from the reconstructions are: (1). The flow pattern of the glacial ice cover of Greenland shows a great resemblance to the present one, the central ice divide being displaced less than 50 km from its present position and being no more than 200 m higher than today. (2). The main ice divide of the ice sheet covering the Canadian Arctic islands (the Innuitian ice sheet) was located over the highlands of eastern Ellesmere Island with local domes positioned over the present ice caps, indicating that even the deep ice of Wisconsin age in these ice caps is of local origin. This is also the case for the Devon Island ice cap. (3). Even in the not very likely case of a rather extensive glacial ice cover in north-west Greenland, the ice-flow pattern upstream of the Camp Century deep drill site would not have changed radically compared to the present flow pattern. Thus it is concluded that even advanced ice margins in late-Wisconsin time could at most have resulted in an elevation of the deposition site of the late-Wisconsin ice at Camp Century 600 m higher than at present. The consequences of this conclusion are discussed.


1995 ◽  
Vol 73 (2) ◽  
pp. 273-284 ◽  
Author(s):  
Claude Ghez ◽  
Robert Sainburg

This paper reviews a series of experiments comparing intact controls with functionally deafferented patients to determine the role of proprioception in controlling dynamic interactions between limb segments during movement. We examine the control of hand path in a planar movement-reversal task and in a familiar three-dimensional gesture with similar biomechanical characteristics. In the planar task subjects had to move their hand out and back along a series of straight-line segments in the horizontal plane without visual feedback. The lengths and directions of the target line segments were chosen to require different amounts of shoulder motion while requiring the same elbow excursion. In controls, hand paths were, as required, straight with sharp bends at the outermost point. In patients, however, distinctive errors appeared at movement reversals, consisting of widened hand paths resulting from desynchronization in the reversals of elbow and shoulder motions. These errors reflected an inability to program elbow muscle contractions in accord with interaction torques produced at the elbow by variations in acceleration of the shoulder. The reversal errors were substantially reduced after patients had practiced for a few trials while visually monitoring movements of their arm. The improvement was not limited to the direction where they had practiced with vision, but also extended to other directions in which the elbow torques were different. This suggests that practice with vision of the arm served to improve the general rules that subjects used to plan movement, rather than simply improving the performance of a specific response. Similar to their performance on the planar task, the patients made errors in interjoint coordination during unconstrained three-dimensional gestures with movement reversals. We conclude (i) that both the planning and the learning of movement required an internal model of the dynamic properties of the limb that takes account of interaction torques acting at different joints; (ii) that this internal model is normally established and updated using proprioceptive information; but (iii) that when proprioception is lacking, vision of the limb in motion partially substitutes for proprioception.Key words: proprioception, multijoint coordination, limb movement, multijoint dynamics, deafferentation.


1925 ◽  
Vol 22 (5) ◽  
pp. 694-699 ◽  
Author(s):  
H. W. Turnbull

§ 1. The six Plücker coordinates of a straight line in three dimensional space satisfy an identical quadratic relationwhich immediately shows that a one-one correspondence may be set up between lines in three dimensional space, λ, and points on a quadric manifold of four dimensions in five dimensional space, S5. For these six numbers pij may be considered to be six homogeneous coordinates of such a point.


1984 ◽  
Vol 5 ◽  
pp. 115-121 ◽  
Author(s):  
N. Reeh

A three-dimensional perfectly plastic ice-sheet model, developed for determining the surface elevations and the flow pattern of an ice sheet with given bottom topography and ice-margin positions, is applied to the reconstruction of the glacial ice covers of Greenland and the Canadian Arctic islands. In the northern regions, two different reconstructions have been performed with ice margins along the present 600 and 200 m sea-depth contours, respectively. In central Greenland, the ice margin is considered to be at the outermost ice-margin deposits on the coastal shelf to the west, and at the present 200 m sea-depth contour to the east.The main conclusions to be drawn from the reconstructions are: (1). The flow pattern of the glacial ice cover of Greenland shows a great resemblance to the present one, the central ice divide being displaced less than 50 km from its present position and being no more than 200 m higher than today. (2). The main ice divide of the ice sheet covering the Canadian Arctic islands (the Innuitian ice sheet) was located over the highlands of eastern Ellesmere Island with local domes positioned over the present ice caps, indicating that even the deep ice of Wisconsin age in these ice caps is of local origin. This is also the case for the Devon Island ice cap. (3). Even in the not very likely case of a rather extensive glacial ice cover in north-west Greenland, the ice-flow pattern upstream of the Camp Century deep drill site would not have changed radically compared to the present flow pattern. Thus it is concluded that even advanced ice margins in late-Wisconsin time could at most have resulted in an elevation of the deposition site of the late-Wisconsin ice at Camp Century 600 m higher than at present. The consequences of this conclusion are discussed.


2005 ◽  
Vol 18 (13) ◽  
pp. 2194-2198 ◽  
Author(s):  
Mikhail Verbitsky

Abstract In an earlier paper by Verbitsky and Saltzman, a vertically integrated, high-resolution, nonlinearly viscous, nonisothermal ice sheet model was presented to calculate the “present-day” equilibrium regime of the Antarctic ice sheet. Steady-state solutions for the ice topography and thermodynamics, represented by the extent of the areas of basal melting, were shown to be in good agreement with both observations and results obtained from other three-dimensional thermodynamical equations. The solution for the basal temperature field of the West Antarctic Siple Coast produced areas at the pressure melting point separated by strips of frozen-to-bed ice, the structure of which looks very similar to ice streams A–E. Since the possible response of the Siple Coast basal temperature pattern to global warming and to associated changes in the snowfall rate is not obvious, a special sensitivity study was conducted. Results of such a study suggest that increased precipitation rate and associated intensification of ice advection can effectively “shut down” West Antarctic ice streams.


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