327
feature, and T increases with both 1J. and N. What observations of the 1982-3 surge of
Variegated Glacier showed, however, was that there is a switch in drainage pattern during
a surge. There are two possible modes of drainage: the Rothlisberger channel described
in section 2 with the value of N determined by the water flow, NR , say; however, if no
channels are present, then water will fill cavities at the bed and leak from one to another.
This is called the linked cavity regime and operates at a higher water pressure and thus
lower effective pressure, Ne , than in the channel drainage. The crucial factor which enables
surges to take place is the switch mechanism, and this depends on the ice flow over the
cavities. If the sliding law is, as discussed in section 2, of the form Tb = N f (1J./ N n ), then
in fact the stresses in the ice are actually determined by 1J./ N n , and in particular the water
stored by cavities depends on this parameter.
It turns out that a simple model of combined water flow through both cavities and a
channel system exhibits instability (the channels close down) if the cavity storage volume
is large enough, and thus the instability occurs at a critical value of A = 1J./ N n , denoted
Ae. It follows from this that a combined model of the drainage system is
N=NR,
1J./N" < Ae;
1J./N n > Ae;
(3.16)
and if this is written as a function N(11.), it is multi-valued, as shown in Fig. 9. As a
consequence of this, the sliding law is indeed multi-valued, and hence Q(H) has the form
shown in Fig. 10.
There are two critical values of Q in fig. 10, denoted Q +, Q _: these are the values
at the noses of the curve (where also H = H+,H_). If s(x) < Q+, then an equilibrium
glacier profile exists in which Q = s(x). However, if the maximum value of s, Smax, is
greater than Q+, then such a stable equilibrium cannot occur, and the glacier surges.
The sequence of events in a surge is then as follows. The glacier grows from a. quiescent
state in which Q < Q+ on the lower (slow) branch everywhere. When the maximum
depth reaches H+, there is a reservoir zone where H > H_. The ice flux at H+ jumps
to the upper (fast) branch by switching drainage pattern, and this switch propagates
upstream and downstream to where H = H_. These activation waves propagate at rates
of hundreds of metres per h01J.r (and in effect ha.ve been observed). Once the activation
waves have propagated to the boundaries of the reservoir zone, it is in the fast mode
on the upper branch, and the activated reservoir zone propagates rapidly downstream,
overriding the stagnant snout and propagating forwards as a front. In terms of fig. 10,
the surge terminates when H reaches H _ everywhere, and deactivation waves propagate
inwards from the boundaries of the exhausted reservoir zone to re-est.ablish the channel
feature, and T increases with both 1J. and N. What observations of the 1982-3 surge of
Variegated Glacier showed, however, was that there is a switch in drainage pattern during
a surge. There are two possible modes of drainage: the Rothlisberger channel described
in section 2 with the value of N determined by the water flow, NR , say; however, if no
channels are present, then water will fill cavities at the bed and leak from one to another.
This is called the linked cavity regime and operates at a higher water pressure and thus
lower effective pressure, Ne , than in the channel drainage. The crucial factor which enables
surges to take place is the switch mechanism, and this depends on the ice flow over the
cavities. If the sliding law is, as discussed in section 2, of the form Tb = N f (1J./ N n ), then
in fact the stresses in the ice are actually determined by 1J./ N n , and in particular the water
stored by cavities depends on this parameter.
It turns out that a simple model of combined water flow through both cavities and a
channel system exhibits instability (the channels close down) if the cavity storage volume
is large enough, and thus the instability occurs at a critical value of A = 1J./ N n , denoted
Ae. It follows from this that a combined model of the drainage system is
N=NR,
1J./N" < Ae;
1J./N n > Ae;
(3.16)
and if this is written as a function N(11.), it is multi-valued, as shown in Fig. 9. As a
consequence of this, the sliding law is indeed multi-valued, and hence Q(H) has the form
shown in Fig. 10.
There are two critical values of Q in fig. 10, denoted Q +, Q _: these are the values
at the noses of the curve (where also H = H+,H_). If s(x) < Q+, then an equilibrium
glacier profile exists in which Q = s(x). However, if the maximum value of s, Smax, is
greater than Q+, then such a stable equilibrium cannot occur, and the glacier surges.
The sequence of events in a surge is then as follows. The glacier grows from a. quiescent
state in which Q < Q+ on the lower (slow) branch everywhere. When the maximum
depth reaches H+, there is a reservoir zone where H > H_. The ice flux at H+ jumps
to the upper (fast) branch by switching drainage pattern, and this switch propagates
upstream and downstream to where H = H_. These activation waves propagate at rates
of hundreds of metres per h01J.r (and in effect ha.ve been observed). Once the activation
waves have propagated to the boundaries of the reservoir zone, it is in the fast mode
on the upper branch, and the activated reservoir zone propagates rapidly downstream,
overriding the stagnant snout and propagating forwards as a front. In terms of fig. 10,
the surge terminates when H reaches H _ everywhere, and deactivation waves propagate
inwards from the boundaries of the exhausted reservoir zone to re-est.ablish the channel