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There are two major ice sheets on the Earth, namely those in Antarctica and Greenland
(the Arctic is an ocean, and its ice is sea ice, rarely more than three metres thick). They
are on the order of thousands of kilometres in extent, and kilometres deep (up to four
for Antarctica). They are thus, in fact, shallow flows, a fact which greatly facilitates the
solution of mathematical models of the flow. Possibly more famous are the ice sheets
which covered much of North America (the Laurentide ice sheet) and northern Europe
(the Fennoscandian ice sheet) during the last ice age. Throughout the Pleistocene era
(that is, the last two million years), there have been a succession of ice ages, each lasting
a typical period of around 90,000 years, during which global ice sheet volume increased,
interspersed with shorter (10,000 year) interglacials, when the ice sheets rapidly retreat.
The last ice age finished some ten thousand years ago, so that we are about due for
another now.
Drainage and sliding
While the motion of ice sheets and glaciers can be understood by means of viscous theory,
there are some notable complications which can occur. Chief among these is that ice can
reach the melting point at the glacier bed, due to frictional heating or geothermal heat
input, in which case water is produced, and the ice can slide. Thus, unlike an ordinary
viscous fluid, slip can occur at the base, and this is determined by a sliding law which
relates basal shear stress T to sliding velocity 1I.b and also, normally, the effective pressure
N = Pi - Pw, where Pi and Pw are ice and water pressures. The determination of Pw
further requires a description of the subglacial hydrology, and thus the dynamics of ice is
intricately coupled to other physical processes: as we shall see, this complexity leads to
some exotic phenomena.
1.2 Waves on glaciers
Just as on rivers, gravity waves will propagate on glaciers. Because the flow is very slow,
they only propagate one way (downstream), and at speeds comparable to the surface speed
(but slightly faster). These waves are known as surface waves, as they are evidenced by
undulations of the surface: an example is shown in Fig. 1. They are examples of kinematic
waves, driven by the dependence of ice flux on glacier depth.
A more exotic kind of wave is the 'seasonal wave'. This has no obvious counterpart in
other fluid flows. It consists of (sizeable) perturbations in the surface velocity field which
propagate down glacier at speeds in the order of 20-150 times the surface speed. There is
no significant surface perturbation, and these waves must in fact be caused by variations
of the basal sliding speed due to annual fluctuations in t.he basal water pressure. Although
well-known and reported at the turn of t.he century, little attention has been paid to these
There are two major ice sheets on the Earth, namely those in Antarctica and Greenland
(the Arctic is an ocean, and its ice is sea ice, rarely more than three metres thick). They
are on the order of thousands of kilometres in extent, and kilometres deep (up to four
for Antarctica). They are thus, in fact, shallow flows, a fact which greatly facilitates the
solution of mathematical models of the flow. Possibly more famous are the ice sheets
which covered much of North America (the Laurentide ice sheet) and northern Europe
(the Fennoscandian ice sheet) during the last ice age. Throughout the Pleistocene era
(that is, the last two million years), there have been a succession of ice ages, each lasting
a typical period of around 90,000 years, during which global ice sheet volume increased,
interspersed with shorter (10,000 year) interglacials, when the ice sheets rapidly retreat.
The last ice age finished some ten thousand years ago, so that we are about due for
another now.
Drainage and sliding
While the motion of ice sheets and glaciers can be understood by means of viscous theory,
there are some notable complications which can occur. Chief among these is that ice can
reach the melting point at the glacier bed, due to frictional heating or geothermal heat
input, in which case water is produced, and the ice can slide. Thus, unlike an ordinary
viscous fluid, slip can occur at the base, and this is determined by a sliding law which
relates basal shear stress T to sliding velocity 1I.b and also, normally, the effective pressure
N = Pi - Pw, where Pi and Pw are ice and water pressures. The determination of Pw
further requires a description of the subglacial hydrology, and thus the dynamics of ice is
intricately coupled to other physical processes: as we shall see, this complexity leads to
some exotic phenomena.
1.2 Waves on glaciers
Just as on rivers, gravity waves will propagate on glaciers. Because the flow is very slow,
they only propagate one way (downstream), and at speeds comparable to the surface speed
(but slightly faster). These waves are known as surface waves, as they are evidenced by
undulations of the surface: an example is shown in Fig. 1. They are examples of kinematic
waves, driven by the dependence of ice flux on glacier depth.
A more exotic kind of wave is the 'seasonal wave'. This has no obvious counterpart in
other fluid flows. It consists of (sizeable) perturbations in the surface velocity field which
propagate down glacier at speeds in the order of 20-150 times the surface speed. There is
no significant surface perturbation, and these waves must in fact be caused by variations
of the basal sliding speed due to annual fluctuations in t.he basal water pressure. Although
well-known and reported at the turn of t.he century, little attention has been paid to these