The topology of ice-sheet centres

AbstractAn ice sheet will, in general, possess points where the horizontal component of velocity is zero, and some of these will be ice centres, occurring close to summits. The paper examines the possible flow patterns near such points. The corresponding horizontal strain-rate pattern is studied by considering an ice sheet which initially has perfect circular symmetry about a vertical axis. Before perturbation there is an isotropic point for the horizontal surface strain rate at the centre. It may be shown, on purely topological grounds and without any reference to the mechanism of flow, that, when the symmetry is broken, this point, being degenerate and structurally unstable, breaks up into two structurally stable components. The breakup always occurs in essentially the same way. Around the two component points the trajectories of principal strain-rate directions always have the lemon pattern. The contours of equal principal strain rate around them are usually hyperbolic; however, if the unperturbed flow pattern had a very pronounced spiral character, they would be elliptic. This behaviour is in contrast to that of the ice centre itself, which remains unsplit.

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

Journal of Glaciology ◽

10.1017/s0022143000015677 ◽

1993 ◽

Vol 39 (131) ◽

pp. 10-14 ◽

Cited By ~ 3

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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Ice Flow along the Byrd Station Strain Network, Antarctica

Journal of Glaciology ◽

10.1017/s0022143000014611 ◽

1979 ◽

Vol 24 (90) ◽

pp. 15-28 ◽

Cited By ~ 39

Author(s):

I. M. Whillans

Keyword(s):

Strain Rate ◽

Isotopic Ratio ◽

Accumulation Rate ◽

Ice Core ◽

Ice Sheet ◽

Surface Strain ◽

Rate Data ◽

Progressive Development ◽

Bed Form ◽

Oxygen Isotopic

AbstractThe flow of the Antarctic ice sheet near Byrd Station is modeled using surface net accumulation-rate data, surface strain-rate data, and core-hole tilting results. The model empirically allows for the progressive development of ice fabric and for values of the vertical strain-rate nearer to zero at depth, and adjusts the strain-rates according to the effect of the climatic warming at the beginning of the Holocene.The validity of the model is supported by the agreements between calculated bed form and that measured by radar sounding, and between calculated and measured present-day ice-sheet thinning-rates. The ice was about 200 m thicker before thinning.The depth-age relationship for the Byrd Station ice core shows that the climatic change represented by the oxygen isotopic ratio of the ice began some 5000 years sooner than in north Greenland (Hammer and others 1978), but ended at about the same time.

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Ice Flow along the Byrd Station Strain Network, Antarctica

Journal of Glaciology ◽

10.3189/s0022143000014611 ◽

1979 ◽

Vol 24 (90) ◽

pp. 15-28 ◽

Cited By ~ 1

Author(s):

I. M. Whillans

Keyword(s):

Strain Rate ◽

Isotopic Ratio ◽

Accumulation Rate ◽

Ice Core ◽

Ice Sheet ◽

Surface Strain ◽

Rate Data ◽

Progressive Development ◽

Bed Form ◽

Oxygen Isotopic

AbstractThe flow of the Antarctic ice sheet near Byrd Station is modeled using surface net accumulation-rate data, surface strain-rate data, and core-hole tilting results. The model empirically allows for the progressive development of ice fabric and for values of the vertical strain-rate nearer to zero at depth, and adjusts the strain-rates according to the effect of the climatic warming at the beginning of the Holocene.The validity of the model is supported by the agreements between calculated bed form and that measured by radar sounding, and between calculated and measured present-day ice-sheet thinning-rates. The ice was about 200 m thicker before thinning.The depth-age relationship for the Byrd Station ice core shows that the climatic change represented by the oxygen isotopic ratio of the ice began some 5000 years sooner than in north Greenland (Hammer and others 1978), but ended at about the same time.

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Topology of fine-scale motions in turbulent channel flow

Journal of Fluid Mechanics ◽

10.1017/s0022112096001802 ◽

1996 ◽

Vol 310 ◽

pp. 269-292 ◽

Cited By ~ 171

Author(s):

Hugh M. Blackburn ◽

Nagi N. Mansour ◽

Brian J. Cantwell

Keyword(s):

Strain Rate ◽

Channel Flow ◽

Velocity Gradient ◽

Outer Region ◽

Turbulent Channel Flow ◽

Principal Strain ◽

Wall Region ◽

Fine Scale ◽

Stable Focus ◽

Topological Features

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

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Rate-dependent ductile fracture under plane strain tension: experiments and simulations

EPJ Web of Conferences ◽

10.1051/epjconf/201818302022 ◽

2018 ◽

Vol 183 ◽

pp. 02022

Author(s):

Vincent Grolleau ◽

Vincent Lafilé ◽

Christian C. Roth ◽

Bertrand Galpin ◽

Laurent Mahéo ◽

...

Keyword(s):

High Strain Rate ◽

Strain Rate ◽

Plane Strain ◽

Static Loading ◽

High Strain ◽

Fracture Initiation ◽

Surface Strain ◽

Experimental Program ◽

Loading Conditions ◽

Plane Strain Tension

Among all other stress states achievable under plane stress conditions, the lowest ductility is consistently observed for plane strain tension. For static loading conditions, V-bending of small sheet coupons is the most reliable way of characterising the strain to fracture for plane strain tension. Different from conventional notched tension specimens, necking is suppressed during V-bending which results in a remarkably constant stress state all the way until fracture initiation. The present DYMAT talk is concerned with the extension of the V-bending technique from low to high strain rate experiments. A new technique is designed with the help of finite element simulations. It makes use of modified Nakazima specimens that are subjected to V-bending. Irrespective of the loading velocity, plane strain tension conditions are maintained throughout the entire loading history up to fracture initiation. Experiments are performed on specimens extracted from aluminum 2024-T3 and dual phase DP450 steel sheets. The experimental program includes quasi static loading conditions which are achieved on a universal testing machine. In addition, high strain rate experiments are performed using a specially-designed drop tower system. In all experiments, images are acquired with two cameras to determine the surface strain history through stereo Digital Image Correlation (DIC). The experimental observations are discussed in detail and also compared with the numerical simulations to validate the proposed experimental technique

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Monstars on Glaciers

Journal of Glaciology ◽

10.3189/s0022143000005153 ◽

1983 ◽

Vol 29 (101) ◽

pp. 70-77 ◽

Cited By ~ 1

Author(s):

J. F. Nye

Keyword(s):

Numerical Simulation ◽

Strain Rate ◽

Tensor Field ◽

Pure Shear ◽

Glacier Surface ◽

Isotropic Point ◽

Different Types ◽

Isolated Points ◽

Principal Directions ◽

Structurally Stable

AbstractIsotropic points are structurally stable features of any complicated field of stress or strain-rate, and therefore will almost always be present on the surface of a glacier. A given isotropic point for strain-rate will belong to one of six different classes, depending on the pattern (lemon, star, or monstar) of principal directions and the contours (ellipses or hyperbolas) of constant principal strain-rate values in its neighbourhood. The central isotropic point on a glacier should theoretically have a monstar pattern, but the contours around it may sometimes be elliptic and sometimes hyperbolic. Nearby, but not coincident with it there will be an isotropic point for stress. This will also have a monstar pattern but, in contrast to the strain-rate point, the contours around it must be hyperbolic. Published examples are consistent with these conclusions. In addition to isotropic points for strain-rate a glacier surface will contain isolated points of pure shear; these also can be classified into six different types. Stable features of this kind give information about the essential structure of a tensor field and form useful points of comparison between observation and numerical simulation.

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Thermoelastic Constitutive Equations for Chemically Hardening Materials

Journal of Applied Mechanics ◽

10.1115/1.3423365 ◽

1974 ◽

Vol 41 (3) ◽

pp. 652-657 ◽

Cited By ~ 16

Author(s):

Bernard W. Shaffer ◽

Myron Levitsky

Keyword(s):

Bulk Modulus ◽

Strain Rate ◽

Chemical Reaction ◽

Constitutive Equations ◽

Strain Energy ◽

Elastic Solid ◽

Time Dependent ◽

Component Model ◽

Two Component ◽

Potential Applications

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

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Strain Rates On Rutford Ice Stream, Antarctica (Abstract)

Annals of Glaciology ◽

10.1017/s0260305500001592 ◽

1986 ◽

Vol 8 ◽

pp. 207

Author(s):

N. Stephenson ◽

C.S.M. Doake

Keyword(s):

Strain Rate ◽

Velocity Gradient ◽

Surface Strain ◽

Lateral Strain ◽

Strain Rate Tensor ◽

Strain Rates ◽

Average Value ◽

Divergent Flow ◽

Ice Stream ◽

Thickness Variations

In a study of the Rutford Ice Stream, strain rates were measured on a transverse section. Magnitudes ranged up to 40 × 10−3 a−1 but were typically in the order of 3 × 10−3 a−1 with an error of 0.1 χ 10−3 a−1. Variations in the strain rate between adjacent stakes of 0.2 χ 10−3 a−1 to 2 × 10−3 a−1 were matched to the thickness variations on the glacier. For each set of three adjacent stakes, the velocity gradient components of the surface strain rate tensor were calculated by assuming that the gradients were linear over the distance between adjacent stakes. When plotted against distance across the ice stream, each strain rate component revealed different aspects of the flow field. The longitudinal strain rate was compressive, with an almost constant magnitude of 10−3 a−1. The lateral strain rate is extensive, with an average value of 1.1 × 10−3 a−1 which agreed with the angle between the divergent flow lines observed on a Landsat image. Peaks in the lateral strain rate, corresponding to longitudinal bands of thicker ice, showed that these thicker bands were spreading more rapidly at the expense of thinner areas. The two velocity gradient components of the shear rate tensor also reflected differences in ice thickness.

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