Weaknesses of present sliding theory

There are a number of processes involved in sliding of ice over a hard bed that are not adequately described in the above theoretical models. An obvious example is the failure to consider frictional forces between rock particles in the basal ice and the underlying bedrock. To study this effect, Iverson et al. (2003) conducted an experiment at the Svartisen Subglacial Laboratory in Norway. The laboratory is situated in a tunnel system in the bedrock beneath Engabreen (the Enga Glacier), an outlet glacier from the Svartisen Ice Cap. The tunnels were excavated for a hydroelectric power project. One inclined tunnel, excavated specifically for scientific studies, leads upward to the base of the glacier, giving access to the bed beneath 210 m of sliding temperate ice. Using this inclined tunnel, Iverson and his colleagues placed an instrumented panel at the base of the glacier. The upper surface of the panel consisted of a 0.09 m2 smooth granite tablet. Debris-laden ice slid across the tablet and the shear traction on it was recorded along with sliding speed, water pressure, and temperatures in the panel. Shear tractions on the panel varied from 60 to 110 kPa, and at one point rose to 200 kPa. The spatially averaged driving stress is estimated to be between 150 and 300 kPa, so the measured shear tractions on the panel were a significant fraction of the total drag. As the tablet was smooth and mounted flush with the fixed edges of the panel, shear tractions on it would presumably have been negligible if the ice had been free of sediment.

Let us explore the reason for the high frictional forces between the panel and the dirty ice. Ice is relatively soft, so one might imagine that a particle imbedded in basal ice would simply be pushed up into the ice rather than exert a sustained high contact force against the bed. However, in a temperate glacier, ice at the bed is melting and some or all of the meltwater may drain away. To replace this loss, ice must flow past the particle toward the bed. As first recognized by Hallet (1979a), it is this flow that drives particles toward the bed and maintains high contact forces between the particles and the bed. This is why glacier beds are striated. As with flow of ice past obstacles on the bed, flow of ice past particles toward the bed can be analyzed in terms of regelation and plastic flow. And as with bumps on the bed, particles of a certain size, ~0.1 m, are forced against the bed more vigorously than smaller or larger particles. The ice moves more readily past smaller particles by regelation and past larger particles by plastic flow.

"Frictional" drag may also occur in areas where ice becomes temporarily frozen to the bed. Robin (1976) proposed two mechanisms for forming such cold patches. In the first, which he termed the "heat pump effect" (Figure 7.6a), water that is formed in the zone of high pressure

High P cold

Ice flow

Low P

Ice warms by freezing meltwater

High P cold

Low P

Ice warms by freezing meltwater

Figure 7.6. Formation of cold patches (after Robin, 1976). (a) Water that is squeezed out of the ice on the stoss side of an obstacle may drain away and thus not be available to refreeze in the low pressure zone at the top of the obstacle. (b) Small changes in pressure between obstacles result in large changes on tops of obstacles.

Figure 7.6. Formation of cold patches (after Robin, 1976). (a) Water that is squeezed out of the ice on the stoss side of an obstacle may drain away and thus not be available to refreeze in the low pressure zone at the top of the obstacle. (b) Small changes in pressure between obstacles result in large changes on tops of obstacles.

Mean pressure is same in both cases: 24.2/11 = 2.2 MPa b—D-

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on the stoss side of a bump, where the melting point is depressed, is squeezed out of the ice through veins formed where three ice crystals abut one another (see Figure 8.1). When this "cold" ice is transported to the top of the bump, where the pressure is less, any water remaining in the ice and along the ice-rock interface refreezes, releasing the heat of fusion and thus warming the ice. The water within the ice is likely to freeze first, followed by that at the interface. If the amount of water present is sufficient, enough heat will be released to warm the ice to the new pressure melting point without freezing all of the water at the interface. However, if some of the melt water escaped around the bump as shown in Figure 7.6a, all of the water at the interface may freeze, thus cementing the glacier to the bed.

The second mechanism discussed by Robin involves local increases in water pressure in areas between bumps. Because the weight of the glacier is constant, any such increase will decrease the pressure on stoss sides of bumps, where the pressure is already higher than average. In the example shown in Figure 7.6b, the area between bumps is 10 times the area of the bumps. Thus a 0.1 MPa increase in pressure between bumps reduces the pressure over the bumps by 1 MPa, resulting in a ~0.7 °C increase in the pressure melting point. The ice, being at the pressure melting point, was colder while the pressure was high. Thus, the decrease in pressure leads to freezing of any water present, potentially including any at the ice-rock interface.

In addition to increasing the drag between the glacier and the bed, such cold patches may be an effective erosional mechanism. Rock fragments that have been loosened from the bed but do not project appreciably above it are separated from the ice by a melt film. As long as the melt film exists, they may be held in the bed by rock-to-rock frictional forces that exceed the drag exerted by the ice through the film. However, such fragments may be entrained if the melt film becomes frozen.

There are also a number of problems surrounding the use of the simple regelation theory presented above. Nye (1973a) notes, for example, that at any point on an obstacle, the melt rate (or freezing rate) required for movement of ice past that obstacle by regelation is completely determined by the geometry of the obstacle, and in particular by the inclination of the face to the direction of motion. The melt rate determines the heat sources and sinks, so the temperature distribution is known, and hence also the pressure distribution. The melting and freezing rates also determine the water fluxes required. The awkward fact is that for normal bed geometries, the pressure distribution predicted by the simple theory commonly does not provide pressure gradients in the melt film that are consistent with the water fluxes required. To resolve this discrepancy, one has to take into consideration spatial variations in the thickness of the melt film and temperature gradients across it.

Impurities provide a second problem for regelation theory. Water moving in a melt film over an obstacle on the bed may absorb ions from the bed or from rock flour between the bed and the ice. Such impurities lower the freezing point. Thus, the temperature in the lee of the obstacle is lower than would be the case with pure water, and the temperature gradient through the obstacle is correspondingly reduced (see Figure 7.2). This reduces the heat flux through the obstacle, and thus reduces Sr.

When impurities collect in the freezing water film in the lee of a bump, fractionation occurs; some of the impurities are carried away by the ice that forms, while the rest remain in the melt film. The steady-state situation is one in which the concentration of impurities in the film is such that the rate of removal of ions from the lee side during freezing equals the influx of ions in water coming from the stoss side of the bump. The impure ice thus formed will melt on the next suitable bump downglacier around which regelation is occurring, and the resulting impure melt water will acquire more impurities. After several such cycles, the concentration of ions in water on the lee sides of obstacles becomes high enough to induce precipitation. The most common such precipitates are CaCO3, but Fe/Mn coatings are also observed. Hallet (1976a, 1979b), Hallet et al. (1978), and Ng and Hallet (2002) have made detailed studies of the calcium carbonate precipitates, and Hallet (1976b) has calculated the degree to which basal sliding over a hypothetical bed composed of sinusoidal waves of a single wavelength would be

"O

"O

Figure 7.7. Effect of solutes on speed of sliding over a sinusoidal bump. (After Hallet, 1976b. Reproduced with permission of the author and the International Glaciological Society.)

Wavelength, m

Wavelength, m

Figure 7.7. Effect of solutes on speed of sliding over a sinusoidal bump. (After Hallet, 1976b. Reproduced with permission of the author and the International Glaciological Society.)

reduced by various concentrations of CaCOj in the melt film (Figure 7.7). Note, in Figure 7.7, that the wavelength for which S is a minimum, that is A.c, is reduced from 0.6 m for the case of no solutes to 0.2 m for the highest solute concentration. This is because solutes reduce the efficacy of the regelation process, effectively shifting the Sr curve in Figure 7.3 downward.

A further effect of solutes has been observed in regelation experiments with wires (Drake and Shreve, 1973). As the stress driving the regelation increases, the pressure in the lee of the wire decreases, and may reach the triple point pressure. At this point a vapor pocket forms and the temperature cannot be raised further. Because the temperature on the stoss side can continue to decrease as the pressure increases, the mean temperature around the wire is less than the far-field temperature, and heat will flow from the surroundings toward the wire. This increases the rate of melting, but also means that some of the melt water formed on the high-pressure side of the wire will not refreeze on the lee side. This water collects in pockets that are then left behind in the ice, resembling a wake, as the wire advances. Such a process might occur beneath glaciers in areas of relatively high basal shear traction.

Finally, the rheology of basal ice may be somewhat different from that of ice well above the bed, thus altering the role of plastic flow, and cavities may form in the lee of obstacles. These effects are discussed next.

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