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Kamb Ice Stream flow history and surge potential
- Hermann Engelhardt, Barclay Kamb
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- Journal:
- Annals of Glaciology / Volume 54 / Issue 63 / 2013
- Published online by Cambridge University Press:
- 26 July 2017, pp. 287-298
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A basal zone, tens of meters thick, of debris-laden ice was observed in Kamb Ice Stream, West Antarctica, using a video camera lowered into boreholes made by hot-water drilling. The debris content varies, sometimes abruptly, forming a sequence of layers that reflect the complex history of fast ice flow and bed interaction. In most parts, the concentration of debris is low, a few percent by weight, with particles, often mud clots, dispersed in a matrix of clear ice. The nature of the debris distribution can be interpreted in terms of specific time intervals in the history of fast motion of Kamb Ice Stream including processes leading up to the termination of its streaming behavior and possible reactivation.
Stress-gradient Coupling in Glacier Flow: IV. Effects of the “T” Term*
- Barclay Kamb, Keith A. Echelmeyer
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- Journal:
- Journal of Glaciology / Volume 32 / Issue 112 / 1986
- Published online by Cambridge University Press:
- 12 May 2017, pp. 342-349
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The “T term” in the longitudinal stress-equilibrium equation for glacier mechanics, a double y-integral of ∂2τxy/∂x2 where x is a longitudinal coordinate and y is roughly normal to the ice surface, can be evaluated within the framework of longitudinal flow-coupling theory by linking the local shear stress τxy at any depth to the local shear stress τB at the base, which is determined by the theory. This approach leads to a modified longitudinal flow-coupling equation, in which the modifications deriving from the T term are as follows: 1. The longitudinal coupling length is increased by about 5%. 2. The asymmetry parameter σ is altered by a variable but small amount depending on longitudinal gradients in ice thickness h and surface slope α. 3. There is a significant direct modification of the influence of local h and α on flow, which represents a distinct “driving force” in glacier mechanics, whose origin is in pressure gradients linked to stress gradients of the type ∂τxy/∂x. For longitudinal variations in h, the “T force” varies as d2h/dx2 and results in an in-phase enhancement of the flow response to the variations in h, describable (for sinusoidal variations) by a wavelength-dependent enhancement factor. For longitudinal variations in α, the “force” varies as dα/dx and gives a phase-shifted flow response. Although the “T force” is not negligible, its actual effect on τB and on ice flow proves to be small, because it is attenuated by longitudinal stress coupling. The greatest effect is at shortest wavelengths (λ 2.5h), where the flow response to variations in h does not tend to zero as it would otherwise do because of longitudinal coupling, but instead, because of the effect of the “T force”, tends to a response about 4% of what would occur in the absence of longitudinal coupling. If an effect of this small size can be considered negligible, then the influence of the T term can be disregarded. It is then unnecessary to distinguish in glacier mechanics between two length scales for longitudinal averaging of τb, one over which the T term is negligible and one over which it is not.
Longitudinal flow-coupling theory also provides a basis for evaluating the additional datum-state effects of the T term on the flow perturbations Δu that result from perturbations Δh and Δα from a datum state with longitudinal stress gradients. Although there are many small effects at the ~1% level, none of them seems to stand out significantly, and at the 10% level all can be neglected.
The foregoing conclusions apply for long wavelengths λh. For short wavelengths (λ h), effects of the T term become important in longitudinal coupling, as will be shown in a later paper in this series.
Flow of Blue Glacier, Olympic Mountains, Washington, U.S.A.*
- Mark F. Meier, W. Barclay Kamb, Clarence R. Allen, Robert P. Sharp
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- Journal:
- Journal of Glaciology / Volume 13 / Issue 68 / 1974
- Published online by Cambridge University Press:
- 30 January 2017, pp. 187-212
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Velocity and strain-rate patterns in a small temperate valley glacier display flow effects of channel geometry, ice thickness, surface slope, and ablation. Surface velocities of 20–55 m/year show year-to-year fluctuations of 1.5–3 m/year. Transverse profiles of velocity have the form of a higher-order parabola modified by the effects of flow around a broad bend in the channel, which makes the velocity profile asymmetric, with maximum velocity displaced toward the outside of the bend. Marginal sliding rates are 5–22 m/year against bedrock and nil against debris. Velocity vectors diverge from the glacier center-line near the terminus, in response to surface ice loss, but converge toward it near the firn line because of channel narrowing. Plunge of the vectors gives an emergence flow component that falls short of balancing ice loss by about 1 m/year. Center-line velocities vary systematically with ice thickness and surface slope. In the upper half of the reach studied, effects of changing thickness and slope tend to compensate, and velocities are nearly constant; in the lower half, the effects are cumulative and velocities decrease progressively down-stream. Where the slope increases down-stream from 7° to 9°, reflecting a bedrock step, there is localized longitudinal extension of 0.03 year–1 followed by compression of 0.08 year–1 where the slope decreases. Marginal shear (up to 0.5 year–1) is strongly asymmetric due to flow around the bend: the stress center-line, where one of the principal axes becomes longitudinal, is displaced 150 m toward the inside of the bend. This effect is prominently visible in the crevasse pattern. Ice fluxes calculated independently by “laminar” flow theory and by continuity disagree in a way which shows that internal deformation of the ice is controlled not by local surface slope but by an effective slope that is nearly constant over the reach studied.
Direct Observation of the Mechanism of Glacier Sliding Over Bedrock*
- Barclay Kamb, E. LaChapelle
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- Journal:
- Journal of Glaciology / Volume 5 / Issue 38 / 1964
- Published online by Cambridge University Press:
- 30 January 2017, pp. 159-172
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At the head of a tunnel driven to bedrock in Blue Glacier, Washington, the mechanism of sliding of the glacier over bedrock has been investigated. This mechanism involves (1) regelation-slip, which operates through the combined action of heat transport and mass transport (liquid and solid) in the immediate neighborhood of the glacier sole; (2) plastic flow, promoted by stress concentrations in the basal ice. We have observed and/or measured the following features of the basal slip process: 1. Slip rate in relation to internal deformation of the ice; 2. Time-variations of the slip rate; 3. Freezing of basal ice to bedrock upon release of overburden pressure; 4. Formation of a regelation layer in the basal ice, and detailed behavior of this layer in relation to bedrock obstacles and to incorporated debris particles; 5. Local separation of ice from bedrock and continuous formation of regelation spicules in the open cavities thus created; 6. Plastic deformation of basal ice as recorded in the warping of foliation planes and of the regelation layer. Simple experiments to test our interpretation of the regelation layer have been carried out, in which regelation flow of solid cubes of different materials frozen into blocks of ice was produced. The field measurements and laboratory results are used to test the theory by Weertman (1957, 1962) of the basal slip mechanism. It is found that the theoretical “controlling obstacle size” and “controlling obstacle spacing” that should correspond to our observations are about an order of magnitude too small. This quantitative failure represents an overemphasis in the theory on the importance of plastic flow as compared to regelation. A new theory has been constructed which gives results in better agreement with observation.
X-Ray Determination of the Structure of Ice IV
- Hermann Engelhardt, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 21 / Issue 85 / 1978
- Published online by Cambridge University Press:
- 30 January 2017, pp. 51-53
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Ice IV, a wholly metastable ice phase, has a structure based on a framework of tetrahedrally hydrogen-bonded water molecules in a rhombohedral unit cell. The structure involves two non-equivalent types of water molecules and four non-equivalent types of hydrogen bonds. A novel structural feature is a hydrogen bond that passes through the center of a 6-ring of water molecules and links non-adjacent structural layers. The bond network is proton-disordered, even after quenching.
Instruments and Methods Glacier Bore-Hole Photography
- W. D. Harrison, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 12 / Issue 64 / 1973
- Published online by Cambridge University Press:
- 30 January 2017, pp. 129-137
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A 51 mm diameter bore-hole camera allows observation of subglacial conditions, measurement of basal sliding rates, and study of internal structure and debris in ice at depth. The camera is simple in construction, field operation and maintenance. Water turbidity is a significant problem but it can be overcome by pumping.
Basal Sliding and Conditions at the Glacier Bed as Revealed by Bore-hole Photography
- H. F. Engelhardt, W. D. Harrison, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 20 / Issue 84 / 1978
- Published online by Cambridge University Press:
- 30 January 2017, pp. 469-508
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Bore-hole photography demonstrates that the glacier bed was reached by cable-tool drilling in five bore holes in Blue Glacier, Washington. Basal sliding velocities measured by bore-hole photography, and confirmed by inclinometry, range from 0.3 to 3.0 cm/d and average 1.0 cm/d, much less than half the surface velocity of 15 cm/d. Sliding directions deviate up to 30° from the surface flow direction. Marked lateral and time variations in sliding velocity occur. The glacier bed consists of bedrock overlain by a ≈ 10 cm layer of active subsole drift, which intervenes between bedrock and ice sole and is actively involved in the sliding process. It forms a mechanically and visibly distinct layer, partially to completely ice-free, beneath the zone of debris-laden ice at the base of the glacier. Internal motions in the subsole drift include rolling of clasts caught between bedrock and moving ice. The largest sliding velocities occur in places where a basal gap, of width up to a few centimeters, intervenes between ice sole and subsole drift. The gap may result from ice—bed separation due to pressurization of the bed by bore-hole water. Water levels in bore holes reaching the bed drop to the bottom when good hydraulic connection is established with sub-glacial conduits; the water pressure in the conduits is essentially atmospheric. Factors responsible for the generally low sliding velocities are high bed roughness due to subsole drift, partial support of basal shear stress by rock friction, and minimal basal cavitation because of low water pressure in subglacial conduits. The observed basal conditions do not closely correspond to those assumed in existing theories of sliding.
The Glide Direction in Ice*
- W. Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 3 / Issue 30 / 1961
- Published online by Cambridge University Press:
- 30 January 2017, pp. 1097-1106
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The failure to detect experimentally a glide direction in the ice crystal is satisfactorily explained by assuming that the crystal glides simultaneously in three symmetry-equivalent directions with a response to the shear stress component in each direction that is the same as that observed for the crystal as a whole or for polycrystalline aggregates—the typical non-linear, power-type flow law. A hexagonal crystal responding to stress by this type of “non-linear crystal viscosity” behaves very differently from a tetragonal one. For a tetragonal crystal, the glide directions are well defined in the response of the crystal if the power-flow-law exponent n exceeds n ~ 1·5, whereas for a hexagonal crystal a well-defined glide direction can be observed only if n > c. 5. The response of a hexagonal crystal is entirely independent of a-axis orientation if n = 3 exactly. For 3 < n < c. 5 the true glide direction should be weakly apparent, whereas for 1 < n < 3 the crystal should show a response weakly suggestive of preferred glide in a direction perpendicular to the true glide direction. In the observed range of n values for ice, 2 < n < 4, the expected response to simultaneous glide differs so slightly from the hitherto-postulated a-axis-independent, “non-crystallographic” glide as to be practically undetectable experimentally. This circumstance makes it possible to identify <>as the glide direction, from structural considerations alone, and to accommodate the plastic properties of the ice crystal into the modern concepts of crystal plasticity. It may be expected that hexagonal close packed and face-centred cubic metals at high temperatures, in steady state creep, will show translation gliding without well-defined glide directions.
Stress-Gradient Coupling in Glacier Flow: I. Longitudinal Averaging of the Influence of Ice Thickness and Surface Slope*
- Barclay Kamb, Keith A. Echelmeyer
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- Journal:
- Journal of Glaciology / Volume 32 / Issue 111 / 1986
- Published online by Cambridge University Press:
- 20 January 2017, pp. 267-284
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For a glacier flowing over a bed of longitudinally varying slope, the influence of longitudinal stress gradients on the flow is analyzed by means of a longitudinal flow-coupling equation derived from the “vertically” (cross-sectionally) integrated longitudinal stress equilibrium equation, by an extension of an approach originally developed by Budd (1968). Linearization of the flow-coupling equation, by treating the flow velocity u (“vertically” averaged), ice thickness h, and surface slope α in terms of small deviations Δu, Δh, and ∆α from overall average (datum) values uo, h0, and α0, results in a differential equation that can be solved by Green’s function methods, giving Δu(x) as a function of ∆h(x) and ∆α(x), x being the longitudinal coordinate. The result has the form of a longitudinal averaging integral of the influence of local h(x) and α(x) on the flow u(x): where the integration is over the length L of the glacier. The ∆ operator specified deviations from the datum state, and the term on which it operates, which is a function of the integration variable x′, represents the influence of local h(x′), α(x′), and channel-shape factor f(x′), at longitudinal coordinate x′, on the flow u at coordinate x, the influence being weighted by the “influence transfer function” exp (−|x′ − x|/ℓ) in the integral.
The quantity ℓ that appears as the scale length in the exponential weighting function is called the longitudinal coupling length. It is determined by rheological parameters via the relationship , where n is the flow-law exponent, η the effective longitudinal viscosity, and η the effective shear viscosity of the ice profile, η is an average of the local effective viscosity η over the ice cross-section, and (η)–1 is an average of η−1 that gives strongly increased weight to values near the base. Theoretically, the coupling length ℓ is generally in the range one to three times the ice thickness for valley glaciers and four to ten times for ice sheets; for a glacier in surge, it is even longer, ℓ ~ 12h. It is distinctly longer for non-linear (n = 3) than for linear rheology, so that the flow-coupling effects of longitudinal stress gradients are markedly greater for non-linear flow.
The averaging integral indicates that the longitudinal variations in flow that occur under the influence of sinusoidal longitudinal variations in h or α, with wavelength λ, are attenuated by the factor 1/(1 + (2πℓ/λ)2) relative to what they would be without longitudinal coupling. The short, intermediate, and long scales of glacier motion (Raymond, 1980), over which the longitudinal flow variations are strongly, partially, and little attenuated, are for λ ≲ 2ℓ , 2ℓ ≲ λ ≲ 20ℓ, and λ ≳ 20ℓ.
For practical glacier-flow calculations, the exponential weighting function can be approximated by a symmetrical triangular averaging window of length 4ℓ, called the longitudinal averaging length. The traditional rectangular window is a poor approximation. Because of the exponential weighting, the local surface slope has an appreciable though muted effect on the local flow, which is clearly seen in field examples, contrary to what would result from a rectangular averaging window.
Tested with field data for Variegated Glacier, Alaska, and Blue Glacier, Washington, the longitudinal averaging theory is able to account semi-quantitatively for the observed longitudinal variations in flow of these glaciers and for the representation of flow in terms of “effective surface slope” values. Exceptions occur where the flow is augmented by large contributions from basal sliding in the ice fall and terminal zone of Blue Glacier and in the reach of surge initiation in Variegated Glacier. The averaging length 4l that gives the best agreement between calculated and observed flow pattern is 2.5 km for Variegated Glacier and 1.8 km for Blue Glacier, corresponding to ℓ/h ≈ 2 in both cases.
If ℓ varies with x, but not too rapidly, the exponential weighting function remains a fairly good approximation to the exact Green’s function of the differential equation for longitudinal flow coupling; in this approximation, ℓ in the averaging integral is ℓ(x) but is not a function of x′. Effects of longitudinal variation of J are probably important near the glacier terminus and head, and near ice falls.
The longitudinal averaging formulation can also be used to express the local basal shear stress in terms of longitudinal variations in the local “slope stress” with the mediation of longitudinal stress gradients.
Basal sliding of Ice Stream B, West Antarctica
- Engelhardt Hermann, Kamb Barclay
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- Journal:
- Journal of Glaciology / Volume 44 / Issue 147 / 1998
- Published online by Cambridge University Press:
- 20 January 2017, pp. 223-230
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A “tethered stake” apparatus is used to measure basal sliding in a borehole on Ice Stream B, West Antaretica, about 300 km upstream (east) from its grounding line near the head of the Ross Ice Shelf. A metal stake, emplaced at the top of a laver of unfrozen till underlying the ice, is connected by a tether line to a metering unit that measures the tether line as it is pulled out from the borehole by the stake as a result of basal sliding. The measured sliding motion includes any actual slip across the ice–till interface and may include in addition a possible contribution from shear deformation of till within about 3 cm of the interface. This 3 cm figure follows from a qualitative model of the movements of the stake in the course of the experiment, based on features of the record of apparent sliding. Alternative but less likely models would increase the figure from 3 cm to 10 cm or 25 cm. In any case it is small compared to the seismically inferred till thickness of 9 m. Measured apparent sliding averages 69% of the total motion of 1.2 m d−1 over 26 days of observation if a 3.5 day period of slow apparent sliding (8% of the total motion) is included in the average. The occurrence of the slow period raises the possibility that the sliding motion switches back and forth between c.80% and c. 8% of the total motion, on a time-scale of a few days. However, it is likely that the period of slow apparent sliding represents instead a period when the stake got caught on the ice sole. If the slow period is therefore omitted, the indicated average basal sliding rate is 83% of the total motion. In either case, basal sliding predominates as the cause of the rapid ice-stream motion. In the last 2 days of observation the average apparent sliding rate reached 1.17 m d−1, essentially 100% of the motion of the ice stream. If till deformation contributes significantly to the ice-stream motion, the contribution is concentrated in a shear zone 3 cm to possibly 25 cm thick at the top of the 9 m thick till layer. These observations, if applicable to the West Antaretic ice sheet in general, pose complications in modeling the rapid ice-streaming motion.
Stress-Gradient Coupling in Glacier Flow:III. Exact Longitudinal Equilibrium Equation*
- Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 32 / Issue 112 / 1986
- Published online by Cambridge University Press:
- 20 January 2017, pp. 335-341
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The “vertically” integrated, exact longitudinal stress-equilibrium equation of Budd (1970) is developed further in such a way as to yield an equation that gives explicitly and exactly the contributions to the basal shear stress made by surface and bed slope, surface curvature, longitudinal stress deviators, and longitudinal stress gradients in a glacier flowing in plane strain over a bed of longitudinally varying slope. With this exact equation, questions raised by various approximate forms of the longitudinal equilibrium equation can be answered decisively, and the magnitude of errors in the approximations can be estimated. To first order, in the angle δ that describes fluctuations in the surface slope α from its mean value, the exact equilibrium equation reduces to
where G and T are the well-known stress-deviator-gradient and “variational stress” terms, K is a “longitudinal curvature” term, and B is a “basal drag” term that contributes a resistance to sliding across basal hills and valleys. Except for T, these terms are expressed in simple form and evaluated for practical situations. The bed slope θ (relative to the mean slope) is not assumed to be small, which allows the effects of bedrock topography to be determined, particularly through their appearance in the B term.
Waves of Accelerated Motion in a Glacier Approaching Surge: the Mini-Surges of Variegated Glacier, Alaska, U.S.A.*
- Barclay Kamb, Hermann Engelhardt
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- Journal:
- Journal of Glaciology / Volume 33 / Issue 113 / 1987
- Published online by Cambridge University Press:
- 20 January 2017, pp. 27-46
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Periods of dramatically accelerated motion, in which the flow velocity increases suddenly from about 55 cm/d to a peak of 100–300cm/d and then decreases gradually over the course of a day, occurred repeatedly during June and July 1978–81 in Variegated Glacier (Alaska), a surging-type glacier that surged in 1982–83. These “mini-surges” appear to be related mechanistically to the main surge. The flow-velocity peak propagates down-glacier as a wave at a speed of about 0.3 km/h, over a reach of about 6 km in length. It is accompanied by a propagating pressure wave in the basal water system of the glacier, in which, after a preliminary drop, the pressure rises rapidly to a level greater than the ice-overburden pressure at the glacier bed, and then drops gradually over a period of 1–2 d, usually reaching a new low for the summer. The peak velocity is accompanied by a peak of high seismic activity due to widespread fresh crevassing. It is also accompanied by a rapid uplift of the glacier surface, amounting to 6–11 cm, which then relaxes over a period of 1–2 d. Maximum uplift rate coincides with the peak in flow velocity; the peak in accumulated uplift lags behind the velocity peak by 2 h. The uplift is mainly due to basal cavitation driven by the high basal water pressure, although the strain wave associated with the mini-surge motion can also contribute. Basal cavitation is probably responsible for the pulse of high turbidity that appears in the terminal outflow stream in association with each mini-surge. In the down-glacier reach, where the mini-surge waves are attenuating, the observed strain wave corresponds to what is expected for the propagating pulse in flow velocity, but in the reach of maximum mini-surge motion the strain wave has a form quite different, possibly related to special features in the mini-surge initiation process from that point up-stream. The flow acceleration in the mini-surges is due to enhanced basal sliding caused by the high basal water pressure and the consequent reduction of bed friction. A preliminary velocity increase shortly before the pressure wave arrives is caused by the forward shove that the main accelerated mass exerts on the ice ahead of it, and the resulting preliminary basal cavitation causes the drop in water pressure shortly before the pressure wave arrives. The mini-surge wave propagation is controlled by the propagation of the water-pressure wave in the basal water-conduit system. The propagation characteristics result from a longitudinal gradient (up-glacier increase) in hydraulic conductivity of the basal water system in response to the up-glacier increase of the basal water pressure in the mini-surge wave. The mini-surge waves are initiated in a succession of areas situated generally progressively up-glacier during the course of the summer season. In these areas, presumably, melt water that has accumulated in subglacial (?) reservoirs is released suddenly into the basal water system immediately below, generating a pressure rise that propagates down-stream from there. Relationships of the mini-surges to the main surge are seen in the role of high basal water pressure in causing the rapid glacier motion in both phenomena, in the pulse-propagation features of both, and in the high outflow turbidity associated with both. The mini-surges of Variegated Glacier have a strong resemblance to movement and uplift events observed in Unteraargletscher and Findelengletscher, Switzerland. This bears on the question whether the mini-surges are a particular characteristic of surge-type glaciers prior to surge.
Stress-Gradient Coupling in Glacier Flow: II. Longitudinal Averaging in the Flow Response to Small Perturbations in Ice Thickness and Surface Slope*
- Keith A. Echelmeyer, Barclay Kamb, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 32 / Issue 111 / 1986
- Published online by Cambridge University Press:
- 20 January 2017, pp. 285-298
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As a result of the coupling effects of longitudinal stress gradients, the perturbations ∆u in glacier-flow velocity that result from longitudinally varying perturbations in ice thickness ∆h and surface slope ∆α are determined by a weighted longitudinal average of ϕh∆h and ϕα∆α, where ϕh and ϕα are “influence coefficients” that control the size of the contributions made by local ∆h and ∆α to the flow increment in the longitudinal average. The values of ϕh and ϕα depend on effects of longitudinal stress and velocity gradients in the unperturbed datum state. If the datum state is an inclined slab in simple-shear flow, the longitudinal averaging solution for the flow perturbation is essentially that obtained previously (Kamb and Echelmeyer, 1985) with equivalent values for the longitudinal coupling length l and with ϕh = n + 1 and ϕα + n, where n is the flow-law exponent. Calculation of the influence coefficients from flow data for Blue Glacier, Washington, indicates that in practice ϕα differs little from n, whereas ϕh can differ considerably from n + 1. The weighting function in the longitudinal averaging integral, which is the Green’s function for the longitudinal coupling equation for flow perturbations, can be approximated by an asymmetric exponential, whose asymmetry depends on two “asymmetry parameters” μ and σ, where μ is the longitudinal gradient of ℓ(= dℓ/dx). The asymmetric exponential has different coupling lengths ℓ+ and ℓ− for the influences from up-stream and from down-stream on a given point of observation. If σ/μ is in the range 1.5–2.2, as expected for flow perturbations in glaciers or ice sheets in which the ice flux is not a strongly varying function of the longitudinal coordinate x, then, when dℓ/dx > 0, the down-stream coupling length ℓ+ is longer than the up-stream coupling length ℓ−, and vice versa when dℓ/dx < 0. Flow-, thickness- and slope-perturbation data for Blue Glacier, obtained by comparing the glacier in 1957–58 and 1977–78, require longitudinal averaging for reasonable interpretation. Analyzed on the basis of the longitudinal coupling theory, with 4ℓ + 1.6 km up-stream, decreasing toward the terminus, the data indicate n to be about 2.5, if interpreted on the basis of a response factor Ѱ + 0.85 derived theoretically by Echelmeyer (unpublished) for the flow response to thickness perturbations in a channel of finite width. The data contain an apparent indication that the flow response to slope perturbations is distinctly smaller, in relation to the response to thickness perturbations, than is expected on a theoretical basis (i.e. ϕα/ ϕh + (n/n + 1) for a slab). This probably indicates that the effective ℓ is longer than can be tested directly with the available data set owing to its limited range in x.
Glacier Flow in a Curving Channel
- Keith Echelmeyer, Kamb Barclay
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- Journal:
- Journal of Glaciology / Volume 33 / Issue 115 / 1987
- Published online by Cambridge University Press:
- 20 January 2017, pp. 281-292
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The flow of a glacier along a channel of constant longitudinal curvature is analyzed using analytical and finite-element methods. Channels of various cross–sectional shape are investigated, ranging from a simple rectangular form with zero shear traction along the bed to realistic profiles taken from Blue Glacier, Washington. Terms in the equilibrium and rate-of-deformation equations which are inversely dependent on radius and a body force which varies transversely across the glacier introduce several characteristic features into the stress and velocity fields of the curving glacier. The stress center line is shifted toward the inside of the bend, causing an asymmetric crevasse pattern and non‒zero stress magnitude at the surface on the geometric center line of the channel. The stress field is dependent on the stress exponent in the flow law and is non-linear across the surface. The surface–velocity pattern shows a “tilting” of the usual high‒order parabolic form, being skewed toward the inside of the bend. There is a shift in the velocity maximum from the deepest part of the channel. All of these curvature‒induced features are dependent on the radius of curvature, actual channel geometry, and stress exponent in the flow law. Model results show excellent agreement with the velocity and crevasse patterns on the curving Blue Glacier.
Basal hydraulic system of a West Antarctic ice stream: constraints from borehole observations
- Hermann Engelhardt, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 43 / Issue 144 / 1997
- Published online by Cambridge University Press:
- 20 January 2017, pp. 207-230
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Pressure and tracer measurements in boreholes drilled to the bottom of Ice Stream B, West Antarctica, are used to obtain information about the basal water conduit system in which high water pressures are developed.These high pressures presumably make possible the rapid movement of the ice stream. Pressure in the system is indicated by the borehole water level once connection to the conduit system is made. On initial connection, here also called “breakthrough” to the basal water system, the water level drops in a few minutes to an initial depth in the range 96–117 m below the surface. These water levels are near but mostly somewhat deeper than the floation level of about 100 m depth (water level at which basal water pressure and ice overburden pressure are equal), which is calculated from depth-density profiles and is measured in one borehole. The conduit system can be modelled as a continuous or somewhat discontinuous gap between ice and bed; the thickness of the gap δ has to be about 2 mm to account for the water-level drop on breakthrough, and about 4 mm to fit the results of a salt-tracer experiment indicating downstream transport at a speed of 7.5 mm s−1. The above gap-conduit model is, however, ruled out by the way a pressure pulse injected into the basal water system at breakthrough propagates outward from the injection hole, and also by the large hole-to-hole variation in measured basal pressure, which if present in a gap-conduit system with δ = 2 or 4 mm would result in unacceptably large local water fluxes. An alternative model that avoids these objections, called the “gap opening” model, involves opening a gap as injection proceeds: starting with a thin film, the injection of water under pressure lifts the ice mass around the borehole, creating a gap 3 or 4mm wide at the ice/bed interface. Evaluated quantitatively, the gap-opening model accounts for the volume of water that the basal water system accepts on breakthrough, which obviates the gap-conduit model. In order to transport basal meltwater from upstream it is then necessary for the complete hydraulic model to contain also a network of relatively large conduits, of which the most promising type is the “canal” conduit proposed theoretically by Walder and Fowler (1994): flat, low conduits incised into the till, ∼0.1 m deep and perhaps ∼1 m wide, with a flat ice roof. The basal water-pressure data suggest that the canals are spaced ∼50–300 m apart, much closer than R-tunnels would be. The deepest observed water level, 117 m, is the most likely to reflect the actual water pressure in the canals, corresponding to a basal effective pressure of 1.6 bar. In this interpretation, the shallower water levels are affected by loss of hydraulic head in the narrow passageway (s) that connect along the bed from borehole to canal(s). Once a borehole has frozen up and any passageways connecting with canals have become closed, a pressure sensor in contact with the unfrozen till that underlies the ice will measure the pore pressure in the till, given enough time for pressure equilibration. This pressure varies considerably with time, over the equivalent water-level range from 100 to 113 m. Basal pressure sensors 500 m apart report uncorrelated variations, whereas sensors in boreholes 25 m араrt report mostly (but not entirely) well-correlated variations, of unknown origin. In part of the record, remarkable anticorrelated variations are interspersed with positively correlated ones, and there are rare, abrupt excursions to extreme water levels as deep as 125 m and as shallow as 74 m. A diurnal pressure fluctuation, intermittently observed, may possibly be caused by the ocean tide in the Ross Sea. The lack of any observed variation in ice-stream motion, when large percentagewise variations in basal effective pressure were occurring according to our data, suggests that the observed pressure variations are sufficiently local, and so randomly variable from place to place, that they are averaged out in the process by which the basal motion of the ice stream is determined by an integration over a large area of the bed.
The marginal shear stress of Ice Stream B, West Antarctica
- Miriam Jackson, Barclay Kamb
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- Journal:
- Journal of Glaciology / Volume 43 / Issue 145 / 1997
- Published online by Cambridge University Press:
- 20 January 2017, pp. 415-426
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To ascertain whether the velocity of Ice Stream B, West Antarctica, may be controlled by the stresses in its marginal shear zones (the “Snake” and the “Dragon”), we undertook a determination of the marginal shear stress in the Dragon near Camp Up B by using ice itself as a stress meter. The observed marginal shear strain rate of 0.14 a−1 is used to calculate the marginal shear stress from the flow law of ice determined by creep tests on ice cores from a depth of 300 m in the Dragon, obtained by using a hot-water ice-coring drill. The test-specimen orientation relative to the stress axes in the tests is chosen on the basis of c-axis fabrics so that the test applies horizontal shear across vertical planes parallel to the margin. The resulting marginal shear stress is (2.2 ± 0.3) × 105 Pa. This implies that 63–100% of the ice stream’s support against gravitational loading comes from the margins and only 37–0% from the base, so that the margins play an important role in controlling the ice-stream motion. The marginal shear-stress value is twice that given by the ice-stream model of Echelmeyer and others (1994) and the corresponding strain-rate enhancement factors differ greatly (E ≈ 1–2 vs 10–12.5). This large discrepancy could be explained by recrystallization of the ice during or shortly after coring. Estimates of the expected recrystallization time-scale bracket the ∼1 h time-scale of coring and leave the likelihood of recrystallization uncertain. However, the observed two-maximum fabric type is not what is expected for annealing recrystallization from the sharp single-maximum fabric that would be expected in situ at the high shear strains involved (γ ∼ 20). Experimental data from Wilson (1982) suggest that, if the core did recrystallize, the prior fabric was a two-maximum fabric not substantially different from the observed one, which implies that the measured flow law and derived marginal shear stress are applicable to the in situ situation. These issues need to be resolved by further work to obtain a more definitive observational assessment of the marginal shear stress.