331
It is not difficult to see from (3.24) if f is low enough (equivalently, the friction
coefficient c is low enough), that 11 and hence the ice flux Q will be a multivalued function
of h, as shown in fig. 11. In fact, application of realistic parameter values suggests that
such multi-valued flux laws are normal.
What then happens in a region such as the Ross ice shelf area? We suppose that the
ice flux is determined by conditions upstream, so that if the ice flux per unit width is g,
and the width of the discharge region is W, then
Wg =s,
(3.26)
where s is the volume flux of ice discharged. Now if s/W < Qc (see fig. ll), then a
uniform slow moving ice flow is possible. Similarly, if s/W > Qm, a uniform fast moving
ice stream is possible. What if Qm. < s/W < Qc? A uniform stream is now unstable,
and we may expect an instability to occur, whereby ice streams spontaneously occur, as
observed. Such an instability would be mediated by transitions in water pressure, since
basal water will flow from fast streams at high water pressure to slower ice at low water
pressure. This generates a lateral enthalpy flux, and in a steady state this can be balanced
by a heat flux in the ice in the opposite direction, since cooling (g) is less effective at lower
71., therefore the slow ice is warmer near the base than the ice streams. No analysis of this
idea has yet been done, though it is an intriguing mathematical problem.
3.4 Heinrich events and the Hudson strait mega- surge
What if the drainage channel of an ice sheet over deforming till is relatively narrow? By
analogy of the pattern formation mechanism in reaction diffusion equations, one would
expect that. a multivalued flux-depth relation would not allow separate streams to form if
the channel width is too small, and in t.his case we would expect periodic surges to occur
down the channel, if the prescribed mass flux lies on the unstable position of fig. 1l.
A situation of this type appears to have occurred during the last ice age. The Laurentide ice sheet which existed in North America drained the ice dome which layover
Hudson Bay out through the Hudson Strait., a 200 km wide trough which discharged the
ice (as icebergs) into the Labrador sea and thence to the North Atlantic.
Hudson Bay is underlain by soft. carbonate rocks, mudstones, which can be mobilised
when wet. It is suggested that the presence of these deformable sediments, together
with the confined drainage channel, led to the occurrence of semi-periodic surges of the
Hudson Strait ice stream. The evolution of event.s is then as follows. When ice is thin
over Hudson Bay, the mudstones are frozen at the base, there is no sliding and very little
ice flow. Consequently, t.he ice thickens and eventually the basal ice warms. The basal
muds thaw, and sliding is initiated. If the friction is sufficiently low, then t.he multi-valued
It is not difficult to see from (3.24) if f is low enough (equivalently, the friction
coefficient c is low enough), that 11 and hence the ice flux Q will be a multivalued function
of h, as shown in fig. 11. In fact, application of realistic parameter values suggests that
such multi-valued flux laws are normal.
What then happens in a region such as the Ross ice shelf area? We suppose that the
ice flux is determined by conditions upstream, so that if the ice flux per unit width is g,
and the width of the discharge region is W, then
Wg =s,
(3.26)
where s is the volume flux of ice discharged. Now if s/W < Qc (see fig. ll), then a
uniform slow moving ice flow is possible. Similarly, if s/W > Qm, a uniform fast moving
ice stream is possible. What if Qm. < s/W < Qc? A uniform stream is now unstable,
and we may expect an instability to occur, whereby ice streams spontaneously occur, as
observed. Such an instability would be mediated by transitions in water pressure, since
basal water will flow from fast streams at high water pressure to slower ice at low water
pressure. This generates a lateral enthalpy flux, and in a steady state this can be balanced
by a heat flux in the ice in the opposite direction, since cooling (g) is less effective at lower
71., therefore the slow ice is warmer near the base than the ice streams. No analysis of this
idea has yet been done, though it is an intriguing mathematical problem.
3.4 Heinrich events and the Hudson strait mega- surge
What if the drainage channel of an ice sheet over deforming till is relatively narrow? By
analogy of the pattern formation mechanism in reaction diffusion equations, one would
expect that. a multivalued flux-depth relation would not allow separate streams to form if
the channel width is too small, and in t.his case we would expect periodic surges to occur
down the channel, if the prescribed mass flux lies on the unstable position of fig. 1l.
A situation of this type appears to have occurred during the last ice age. The Laurentide ice sheet which existed in North America drained the ice dome which layover
Hudson Bay out through the Hudson Strait., a 200 km wide trough which discharged the
ice (as icebergs) into the Labrador sea and thence to the North Atlantic.
Hudson Bay is underlain by soft. carbonate rocks, mudstones, which can be mobilised
when wet. It is suggested that the presence of these deformable sediments, together
with the confined drainage channel, led to the occurrence of semi-periodic surges of the
Hudson Strait ice stream. The evolution of event.s is then as follows. When ice is thin
over Hudson Bay, the mudstones are frozen at the base, there is no sliding and very little
ice flow. Consequently, t.he ice thickens and eventually the basal ice warms. The basal
muds thaw, and sliding is initiated. If the friction is sufficiently low, then t.he multi-valued