Sliding with Cavity Formation

1987 ◽  
Vol 33 (115) ◽  
pp. 255-267 ◽  
Author(s):  
A. C. Fowler
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Power Law ◽  
Drainage System ◽  
Cavity Formation ◽  
Effective Pressure ◽  
Dynamic Phenomenon ◽  
Basal Shear ◽  
Tunnel System

AbstractWe present a model for the determination of a sliding law in the presence of subglacial cavitation. This law determines the basal stress at a clean ice‒bedrock interface in terms of the velocity and effective pressure. The method is based on an exact solution of the Nye—Kamb (linearly viscous) sliding problem with cavities, and uses ideas of Lliboutry (1979) to construct, via renormalization methods, an approximate law for general bedrock form. We show that, for a bedrock whose spectrum has a power‒law behaviour, one obtains a sliding law which gives the basal shear stress proportional to a power of the velocity, and to a power of the effective pressure.The effect of subglacial cavitation on the drainage system is examined, using recent ideas of Kamb. For sufficiently high velocities, drainage through a Röthlisberger tunnel system is unstable, and drainage takes place through the linked system of cavities. This leads to a reduction of the effective pressure, and by taking account of this, one can rewrite the sliding law in terms of stress and velocity only.This sliding law can be multi‒valued, and it is suggested that this underlies the dynamic phenomenon of surges.

scholarly journals Sliding with Cavity Formation

1987 ◽  
Vol 33 (115) ◽  
pp. 255-267 ◽  
Author(s):  
A. C. Fowler
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Power Law ◽  
Drainage System ◽  
Cavity Formation ◽  
Effective Pressure ◽  
Dynamic Phenomenon ◽  
Basal Shear ◽  
Tunnel System

AbstractWe present a model for the determination of a sliding law in the presence of subglacial cavitation. This law determines the basal stress at a clean ice‒bedrock interface in terms of the velocity and effective pressure. The method is based on an exact solution of the Nye—Kamb (linearly viscous) sliding problem with cavities, and uses ideas of Lliboutry (1979) to construct, via renormalization methods, an approximate law for general bedrock form. We show that, for a bedrock whose spectrum has a power‒law behaviour, one obtains a sliding law which gives the basal shear stress proportional to a power of the velocity, and to a power of the effective pressure.The effect of subglacial cavitation on the drainage system is examined, using recent ideas of Kamb. For sufficiently high velocities, drainage through a Röthlisberger tunnel system is unstable, and drainage takes place through the linked system of cavities. This leads to a reduction of the effective pressure, and by taking account of this, one can rewrite the sliding law in terms of stress and velocity only.This sliding law can be multi‒valued, and it is suggested that this underlies the dynamic phenomenon of surges.

scholarly journals Steady flow of a power law fluid through a tapered non-symmetric stenotic tube

2019 ◽  
Vol 4 (1) ◽  
pp. 255-266 ◽  
Author(s):  
Riaz Ahmad ◽  
Asma Farooqi ◽  
Jiazhong Zhang ◽  
Nasir Ali
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Steady Flow ◽  
Power Law ◽  
Governing Equation ◽  
Axial Velocity ◽  
Shear Thickening ◽  
Power Law Fluid ◽  
Shear Thickening Fluid ◽  
Parameters Of Interest

AbstractA steady flow of a power law fluid through an artery with a stenosis has been analyzed. The equation governing the flow is derived under the assumption of mild stenosis. An exact solution of the governing equation is obtained, which is then used to study the effects of various parameters of interest on axial velocity, resistance to flow and shear stress distribution. It is found that axial velocity increases while resistance to flow decreases when going from shear-thinning to shear-thickening fluid. Moreover, the magnitude of shear stress decreases by increasing the tapering parameter. This problem was already addressed by Nadeem et al. [14], but the results presented by them were erroneous due to a mistake in the derivation of the governing equation of the flow. This mistake is highlighted in the "Formulation of the Problem" section.

scholarly journals Water-Pressure Coupling of Sliding and Bed Deformation: I. Water System

1989 ◽  
Vol 35 (119) ◽  
pp. 108-118 ◽  
Author(s):  
R.B. Alley
Keyword(s):  
Shear Stress ◽  
Water Supply ◽  
Water Pressure ◽  
Water System ◽  
Effective Pressure ◽  
Bed Deformation ◽  
Varying Thickness ◽  
Melt Water ◽  
Basal Shear

AbstractAnalysis of the likely behavior of a water system developed between ice and an unconsolidated glacier bed suggests that, in the absence of channelized sources of melt water, the system will approximate a film of varying thickness. The effective pressure in such a film will be proportional to the basal shear stress but inversely proportional to the fraction of the bed occupied by the film. These hypotheses allow calculation of the sliding and bed-deformation velocities of a glacier from the water supply and basal shear stress, as discussed in the second and third papers in this series.

Rheometric Tests and Extrusion

1951 ◽  
Vol 24 (3) ◽  
pp. 520-540
Author(s):  
Silvio Eccher
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Laminar Flow ◽  
Experimental Determination ◽  
Power Law ◽  
Reasonable Agreement ◽  
Straight Line ◽  
Flow Through ◽  
The Relationship

Abstract A cylindrical rheometer of the Couette type, suitable for the experimental determination of the rheological properties of extruded materials, was designed to provide data which could not be obtained with existing plastometers. The purpose of this study was strictly practical, as the work was performed in connection with a study of extruders. The results obtained on twenty-five different materials—natural and synthetic rubbers and compounds of both with various fillers—are reported; measurements fall within shear rate limits from 1 to 100 seconds−1. In this interval the relationship between logD (rate of shear) and logτ (shear stress) is nearly a straight line. It may, therefore, be analytically interpreted by the power law : D=−(τ/c)n, where n and c are parameters characteristic of the material. As the power law is known to be of limited validity, attempts were made to ascertain the limits of its application in laminar flow through a cylindrical hole. The results of measurements carried out on a 2-inch extruder and employing the same materials as were tested by the rheometer are reported. Measurements of pressure and flow were made, using discharge holes of various diameters and operating the screw at various speeds. Reasonable agreement was found between values of flow and pressure determined with an extruder and those calculated from parameters n and c determined with the cylindrical rheometer.

scholarly journals Application of a general sliding law to simulating flow in a glacier cross-section

1992 ◽  
Vol 38 (128) ◽  
pp. 182-190 ◽  
Author(s):  
Jonathan M. Harbor
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Empirical Data ◽  
Effective Pressure ◽  
Land Form ◽  
Development Models ◽  
Basal Sliding ◽  
Basal Shear ◽  
Form Development ◽  
Glacier Motion

AbstractObservations at Athabasca Glacier and elsewhere suggest that basal sliding can account for a very significant part of total glacier motion, and that sliding rates vary significantly across a glacier section. The ability to model such spatial variations in basal velocities is important in understanding flow in valley glaciers, as well as in predicting spatial patterns of glacial erosion that drive land-form development models. With a sliding law in which the basal velocity is dependent on the basal shear stress and inversely dependent on the effective pressure at the bed, it is possible to predict an overall flow pattern that is consistent with the empirical data, if it is assumed that friction increases close to the margin of a glacier.

scholarly journals Water-pressure Coupling of Sliding and Bed Deformation: III. Application to Ice Stream B, Antarctica

1989 ◽  
Vol 35 (119) ◽  
pp. 130-139 ◽  
Author(s):  
R.B. Alley ◽  
D.D. Blankenship ◽  
S.T. Rooney ◽  
C.R. Bentley
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Water Pressure ◽  
Effective Pressure ◽  
West Antarctica ◽  
Bed Deformation ◽  
Ice Stream ◽  
Basal Sliding ◽  
Ice Stream B ◽  
Basal Shear

AbstractGeophysical studies and glaciological analyses suggest strongly that Ice Stream B, West Antarctica, moves primarily by pervasive deformation of a meters thick subglacial till. Analysis of the longitudinal profile of the ice stream up-stream of the ice plain suggests that basal sliding is slow everywhere, that effective pressure decreases slowly down-stream, and that the strain-rate of pervasive shear is proportional to the basal shear stress and inversely proportional to the square or cube of the effective pressure. Discrete shearing may occur beneath the pervasively deforming zone. These and other hypotheses, which build on the analyses of the first two papers in this series, can be tested in the field.

scholarly journals Application of a general sliding law to simulating flow in a glacier cross-section

1992 ◽  
Vol 38 (128) ◽  
pp. 182-190 ◽  
Author(s):  
Jonathan M. Harbor
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Empirical Data ◽  
Effective Pressure ◽  
Land Form ◽  
Development Models ◽  
Basal Sliding ◽  
Basal Shear ◽  
Form Development ◽  
Glacier Motion

AbstractObservations at Athabasca Glacier and elsewhere suggest that basal sliding can account for a very significant part of total glacier motion, and that sliding rates vary significantly across a glacier section. The ability to model such spatial variations in basal velocities is important in understanding flow in valley glaciers, as well as in predicting spatial patterns of glacial erosion that drive land-form development models. With a sliding law in which the basal velocity is dependent on the basal shear stress and inversely dependent on the effective pressure at the bed, it is possible to predict an overall flow pattern that is consistent with the empirical data, if it is assumed that friction increases close to the margin of a glacier.

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