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Journal ArticleDOI

Sliding motion of glaciers: Theory and observation

01 Nov 1970-Reviews of Geophysics (John Wiley & Sons, Ltd)-Vol. 8, Iss: 4, pp 673-728
TL;DR: In this article, the sliding motion of glacier ice over bedrock, which contributes about half the flow velocity of temperate glaciers, is analyzed for arbitrary bedrock topography of low roughness.
Abstract: The sliding motion of glacier ice over bedrock, which contributes about half the flow velocity of temperate glaciers, is analyzed for arbitrary bedrock topography of low roughness. Fourier-analyzed topography is represented by a roughness spectral function ζ(h, k) defined in terms of the mean square topographic amplitude. From an essentially exact solution of the sliding problem for linear ice-flow rheology, an approximate solution for the actual nonlinear rheology is built on the assumption that the second strain-rate invariant depends only on distance from the ice-bedrock contact. The transition wavelength λ0 between regelation and plastic flow, constant in the linear theory, is replaced in the nonlinear theory by a velocity- and roughness-dependent parameter λα that plays a similar role. Detailed results are given for three special types of ζ(h, k): (1) white roughness (|ζ| constant); (2) truncated white roughness (|ζ| constant for all wavelengths above a certain lower limit); (3) a single wavelength; and (4) cross-corrugated sinusoidal waves. The results are tested against field observations of sliding. Given sliding velocity υ, basal shear stress τ, and rheological parameters, the theory predicts roughness values ζ for the different types of ζ(h, k). When compared with ζ values inferred from observed bedrock outcrops, predicted values for white roughness are somewhat too small, whereas for white roughness truncated at 3.53 meters, they are of the expected size (ζ ∼ 0.05). Predicted λα values range from 3 to 112 cm; high υ (>20 m yr−1) generally gives λα in the range 10–40 cm, and low υ (<6 m yr−1) 30–70 cm. The predicted thickness of the regelation layer (1–10 mm) agrees with observation, but the predicted λα values appear to be somewhat too small. Extensive separation of the ice sole from bedrock, due to tensile stresses set up in sliding, is predicted in icefalls, whereas for valley glaciers little separation is predicted, unless meltwater under a head of pressure comparable to half the glacier thickness has access to the bed. Extensive separation is not needed to account for typical sliding velocities, provided that the roughness spectrum is truncated. Observed features of glaciated bedrock indicate truncation, which results from glacial abrasion. For the truncated spectrum, the predicted dependence of υ on τ is much more highly nonlinear than for the full white spectrum; this implies a relatively high sensitivity of sliding velocity to changes in glacier thickness or surface slope.
Citations
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Journal ArticleDOI
TL;DR: In this article, a model of the surge mechanism is developed in terms of a transition from the normal tunnel configuration of the basal water conduit system to a linked cavity configuration that tends to restrict the flow of water, resulting in increased basal water pressures that cause rapid basal sliding.
Abstract: Based on observations of the 1982–1983 surge of Variegated Glacier, Alaska, a model of the surge mechanism is developed in terms of a transition from the normal tunnel configuration of the basal water conduit system to a linked cavity configuration that tends to restrict the flow of water, resulting in increased basal water pressures that cause rapid basal sliding. The linked cavity system consists of basal cavities formed by ice-bedrock separation (cavitation), ∼1 m high and ∼10 m in horizontal dimensions, widely scattered over the glacier bed, and hydraulically linked by narrow connections where separation is minimal (separation gap ≲ 0.1 m). The narrow connections, called orifices, control the water flow through the conduit system; by throttling the flow through the large cavities, the orifices keep the water flux transmitted by the basal water system at normal levels even though the total cavity cross-sectional area (∼200 m^2) is much larger than that of a tunnel system (∼10 m^2). A physical model of the linked cavity system is formulated in terms of the dimensions of the “typical” cavity and orifice and the numbers of these across the glacier width. The model concentrates on the detailed configuration of the typical orifice and its response to basal water pressure and basal sliding, which determines the water flux carried by the system under given conditions. Configurations are worked out for two idealized orifice types, step orifices that form in the lee of downglacier-facing bedrock steps, and wave orifices that form on the lee slopes of quasisinusoidal bedrock waves and are similar to transverse “N channels.” The orifice configurations are obtained from the results of solutions of the basal-sliding-with-separation problem for an ice mass constituting of linear half-space of linear rheology, with nonlinearity introduced by making the viscosity stress-dependent on an intuitive basis. Modification of the orifice shapes by melting of the ice roof due to viscous heat dissipation in the flow of water through the orifices is treated in detail under the assumption of local heat transfer, which guarantees that the heating effects are not underestimated. This treatment brings to light a melting-stability parameter Ξ that provides a measure of the influence of viscous heating on orifice cavitation, similar but distinct for step and wave orifices. Orifice shapes and the amounts of roof meltback are determined by Ξ. When Ξ ≳ 1, so that the system is “viscous-heating-dominated,” the orifices are unstable against rapid growth in response to a modest increase in water pressure or in orifice size over their steady state values. This growth instability is somewhat similar to the jokulhlaup-type instability of tunnels, which are likewise heating-dominated. When Ξ ≲ 1, the orifices are stable against perturbations of modest to even large size. Stabilization is promoted by high sliding velocity ν, expressed in terms of a ν^(−½) and ν^(−1) dependence of Ξ for step and wave cavities. The relationships between basal water pressure and water flux transmitted by linked cavity models of step and wave orifice type are calculated for an empirical relation between water pressure and sliding velocity and for a particular, reasonable choice of system parameters. In all cases the flux is an increasing function of the water pressure, in contrast to the inverse flux-versus-pressure relation for tunnels. In consequence, a linked cavity system can exist stably as a system of many interconnected conduits distributed across the glacier bed, in contrast to a tunnel system, which must condense to one or at most a few main tunnels. The linked cavity model gives basal water pressures much higher than the tunnel model at water fluxes ≳1 m^(3/s) if the bed roughness features that generate the orifices have step heights or wave amplitudes less than about 0.1 m. The calculated basal water pressure of the particular linked cavity models evaluated is about 2 to 5 bars below ice overburden pressure for water fluxes in the range from about 2 to 20 m^(3/s), which matches reasonably the observed conditions in Variegated Glacier in surge; in contrast, the calculated water pressure for a single-tunnel model is about 14 to 17 bars below overburden over the same flux range. The contrast in water pressures for the two types of basal conduit system furnishes the basis for a surge mechanism involving transition from a tunnel system at low pressure to a linked cavity system at high pressure. The parameter Ξ is about 0.2 for the linked cavity models evaluated, meaning that they are stable but that a modest change in system parameters could produce instability. Unstable orifice growth results in the generation of tunnel segments, which may connect up in a cooperative fashion, leading to conversion of the linked cavity system to a tunnel system, with large decrease in water pressure and sliding velocity. This is what probably happens in surge termination. Glaciers for which Ξ ≲ 1 can go into surge, while those for which Ξ ≳ 1 cannot. Because Ξ varies as α^(3/2) (where α is surface slope), low values of Ξ are more probable for glaciers of low slope, and because slope correlates inversely with glacier length in general, the model predicts a direct correlation between glacier length and probability of surging; such a correlation is observed (Clarke et al., 1986). Because Ξ varies inversely with the basal shear stress τ, the increase of τ that takes place in the reservoir area in the buildup between surges causes a decrease in Ξ there, which, by reducing Ξ below the critical value ∼1, can allow surge initiation and the start of a new surge cycle. Transition to a linked cavity system without tunnels should occur spontaneously at low enough water flux, in agreement with observed surge initiation in winter.

666 citations

Journal ArticleDOI
01 Feb 1985-Science
TL;DR: The behavior of the glacier in surge has many remarkable features, which can provide clues to a detailed theory of the surging process and is akin to a proposed mechanism of overthrust faulting.
Abstract: The hundredfold speedup in glacier motion in a surge of the kind the kind that took place in Variegated Glacier in 1982-1983 is caused by the buildup of high water pressure in the basal passageway system, which is made possible by a fundamental and pervasive change in the geometry and water-transport characteristics of this system. The behavior of the glacier in surge has many remarkable features, which can provide clues to a detailed theory of the surging process. The surge mechanism is akin to a proposed mechanism of overthrust faulting.

630 citations

Journal ArticleDOI
TL;DR: The physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community are described in this paper, where a number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.
Abstract: The surface of ice exhibits the swath of phase-transition phenomena common to all materials and as such it acts as an ideal test bed of both theory and experiment. It is readily available, transparent, optically birefringent, and probing it in the laboratory does not require cryogenics or ultrahigh vacuum apparatus. Systematic study reveals the range of critical phenomena, equilibrium and nonequilibrium phase-transitions, and, most relevant to this review, premelting, that are traditionally studied in more simply bound solids. While this makes investigation of ice as a material appealing from the perspective of the physicist, its ubiquity and importance in the natural environment also make ice compelling to a broad range of disciplines in the Earth and planetary sciences. In this review we describe the physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community. A number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.

627 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the relationship between water pressure and velocity and found that fluctuating bed separation was responsible for the velocity variations of water pressure, such as diurnal variations, were usually similar at different locations and in phase.
Abstract: During the snow-melt season of 1982, basal water pressure was recorded in 11 bore holes communicating with the subglacial drainage system In most of these holes the water levels were at approximately the same depth (around 70 m below surface) The large variations of water pressure, such as diurnal variations, were usually similar at different locations and in phase In two instances of exceptionally high water pressure, however, systematic phase shifts were observed; a wave of high pressure travelled down-glacier with a velocity of approximately 100 m/h The glacier-surface velocity was measured at four lines of stakes several times daily The velocity variations correlated with variations in subglacial water pressure The functional relationship of water pressure and velocity suggests that fluctuating bed separation was responsible for the velocity variations The empirical functional relationship is compared to that of sliding over a perfectly lubricated sinusoidal bed On the basis of the measured velocity-pressure relationship, this model predicts a reasonable value of bed roughness but too high a sliding velocity and unstable sliding at too low a water pressure The main reason for this disagreement is probably the neglect of friction from debris in the sliding model The measured water pressure was considerably higher than that predicted by the theory of steady flow through straight cylindrical channels near the glacier bed Possible reasons are considered The very large disagreement between measured and predicted pressure suggests that no straight cylindrical channels may have existed

561 citations

Journal ArticleDOI
TL;DR: In this article, the effect of a variable subglacial water pressure on the sliding velocity of a glacier has been studied using an idealized numerical model in particular the transient stages of growing or shrinking water-filled cavities at the ice-bedrock interface.
Abstract: In order to interpret observed short-term variations of the sliding velocity of a glacier the effect of a variable subglacial water pressure on the sliding velocity has been studied using an idealized numerical model In particular the transient stages of growing or shrinking water-filled cavities at the ice-bedrock interface were analysed It was found that the sliding velocity was larger when cavities were growing than when they had reached the steady-state size for a given water pressure The smallest sliding velocities occurred while cavities were shrinking When cavitation is substantial a small drop of water pressure below the steady-state value (eg by 05 bar) can temporarily cause backward sliding A limiting water pressure at which sliding becomes unstable is derived The consequences of more realistic assumptions than those of the model are discussed

369 citations

References
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BookDOI
01 Jan 1966

1,316 citations

Journal ArticleDOI
TL;DR: In this article, a model is proposed to explain the sliding of any glacier whose bottom surface is at the pressure melting point, and two mechanisms are considered: pressure melting and creep rate enhancement through stress concentrations.
Abstract: A model is proposed to explain the sliding of any glacier whose bottom surface is at the pressure melting point. Two mechanisms are considered. One is pressure melting and the other is creep rate enhancement through stress concentrations. Neither of the mechanisms operating alone is sufficient to explain sliding. If both mechanisms operate together appreciable sliding can occur.

676 citations

Book ChapterDOI
01 Jan 1962

669 citations

Journal ArticleDOI
TL;DR: A total of 204 surging glaciers has been identified in western North America as discussed by the authors, and these glaciers surge repeatedly and probably with uniform periods (from about 15 to greater than 100 years).
Abstract: A total of 204 surging glaciers has been identified in western North America. These glaciers surge repeatedly and probably with uniform periods (from about 15 to greater than 100 years). Ice flow r...

442 citations

Journal ArticleDOI
TL;DR: In this article, a more realistic model of the bed consisting of a superposition of sine waves all having the same roughness r, and a decreasing in a geometrical progression is considered.
Abstract: Earlier theories of Weertman and the present author are reviewed and compared; both are insufficient to account for the facts observed at the tongue of the Allalingletscher. A calculation of the stresses and heat flow at the bed of a glacier with a sinusoidal profile is given which takes account of any degree of subglacial cavitation. The sliding due to plasticity and that due to pressure melting are related to this degree of cavitation and it is shown that these two terms are additive. There results an expression for the friction f ω in terms of the total sliding velocity u and the height of the bumps a. For a given and large enough value of u, f ω (a) exhibits two maxima which are equal and independent of u. The paper then considers a more realistic model of the bed consisting of a superposition of sine waves all having the same roughness r, and a decreasing in a geometrical progression. The biggest a may be inferred from the overall profile of the bedrock; the resulting frictional force can be regarded either as part of the total frictional force f in an overall view for which f = ρgh sin α holds, or else as a correction to such a value on the small scale (the best point of view for crevasse studies). To a first approximation Coulomb’s law of friction holds provided one takes account of the interstitial water pressure at the ice-rock interface. This interstitial pressure p is next related to the thickness of the glacier h. If the subglacial hydraulic system is at atmospheric pressure, p is proportional to h. Next, if the sliding velocity is not too large, the surface slope approaches 1.6r ≈ 0.12 and kinematic waves (which move four times as fast as the ice) disappear rapidly. If the hydraulic system is not at atmospheric pressure the surface slope is smaller and flow instabilities can occur.

408 citations