Size and location of water conduits on eskers

It is natural to assume, as a first approximation, that the tunnel within which an esker formed was comparable in size to the esker (Figure 8.28a). This is consistent with the observation that some eskers are composed of coarse gravel with a dearth of sedimentary structures. However, this

Figure 8.28. Esker of height Ah with: (a) conduit comparable in size to esker; (b) small conduit on top of esker; and (c) small conduit low on side of esker.

Figure 8.28. Esker of height Ah with: (a) conduit comparable in size to esker; (b) small conduit on top of esker; and (c) small conduit low on side of esker.

may be a poor assumption in many instances, as the flux of water implied by a tunnel of this size would be horrendous. As basal melt rates are relatively low, such high fluxes would require either collection of water from a very large area of the bed or a surficial source. In some areas the former is improbable as the drainage area between the heads of eskers and inferred ice divides is insufficient. Likewise, surficial sources many tens of kilometers from the glacier margin are problematical, as near-surface ice temperatures are likely to be well below 0 °C at these elevations, and it is not clear how moulins could develop through a thick cold surface layer.

An alternative is that the tunnel was comparatively small (Figure 8.28b). This might further suggest that the esker formed slowly over a period of many years.

If the tunnel is small compared with the size of the esker, it is also of interest to determine whether it is on top of the esker or low on the side (Figure 8.28c). The intersections of upglacier-dipping equipoten-tial planes with an esker will be convex down-flow, as in a ridge, and streams are not noted for flowing along ridge crests. This suggests that the conduits should be low on the side of the esker. However, one might then expect eskers to be broad-crested and low rather than sharp-crested and high, as is commonly the case.

Shreve (1985a) suggests that debris washed from the crest of the esker down the flank, together with that released from ice near the bed, which has a higher debris content, will accumulate on the lower side of the conduit, at A in Figure 8.28c. Melting will then be concentrated at B and the conduit will migrate back to the top of the esker. He visualizes a situation in which the conduit spends most of the time on top of the esker, but periodically slips down one flank or another and then migrates back to the top. However, the steepest potential gradient would still be away from the esker so it is not clear why the conduit would migrate back up onto the esker rather than laterally away from it, leaving a sheet of gravel in its wake.

Alternatively, this problem can be addressed using the following argument, adapted from (Lliboutry, 1983). If the height ofthe esker is Ah

(Figure 8.28), and there are two channels that are connected hydraulically, one on top of the esker and one on the side, then:

The pressure causing tunnel closure is Pc = Pi — Pw, so subtracting the first of Equations (8.26) from the second:

Now, from Equation (8.18), holding all other factors constant and using n = 3, we find that Q a Pc12. Thus:

- Ptop -c

12

r pcside + (pw-Pi)gAh-

12

p side

P side

Qtop

Qside

Thus, Qtop > Qslde so the conduit on top of the esker will expand at the expense of that on the side. Phrased differently, owing to the nonlinearity of the flow law, the increase in potential closure rate as one moves down off the esker is not offset by the increase in Pw,so closure rates are higher in the conduit on the side, and water in it is forced up onto the top of the esker.

The model of Figure 8.28b is consistent with the observation that sedimentary stratification in eskers is commonly discontinuous, both laterally and longitudinally. The stratification, defined by variations in grain size, could be produced by transverse variations in conduit height combined with lateral migration of the conduit even if flow through the conduit were steady. Pseudoanticlinal bedding is also commonly observed, with beds mimicking the transverse profile of the esker. Such a form would be likely if the conduit periodically slipped down the flank and then migrated back to the crest as Shreve suggested.

In summary, although questions remain, the shape and stratigraphy of sharp-crested eskers suggest that some combination of the processes Shreve identified and those summarized by Equations (8.26) probably result in a tendency for conduits to be on tops of eskers, despite the potential gradient favoring positions on the flanks.

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