240
sustained time on the final thickness pro-
file become negligible. The plot does
200
show, though, that even with an instan-
taneous discharge peak, the effects of ice
0 min
10
160
momentum are important.
20
Figure 65 presents the changes in the
40
80
120
final thickness profile with increased ts
infinite
for the 0.0005 bed slope. The increase in
80
ts results in a slight smoothing and fur-
0
100
200
300
400
500
600
ther thickening of the downstream
Time (min)
reaches. Even for the instantaneous
Figure 63. Inflow hydrographs for various
peak, however, the jam thickness in the
times of sustained flow.
upstream reaches is significantly greater
than the equilibrium value of 1.7 m.
1.6
SUMMARY
1.4
η
η eq
It is well known that ice jams are in-
Bed Slopes
1.2
herently unsteady events, in which mov-
0.00100
ing ice is brought to rest as accumula-
0.00050
0.00005
tions that shove and thicken in accor-
1.0
dance with changing forces exerted by
0
5
10
15
20
ts
water flow, accumulation weight, and
tb
bank roughness. These processes are
Figure 64. Dimensionless jam thickness vs. even more unsteady when a jam col-
ts/tb at three bed slopes.
lapses, plows downstream, and possibly
reforms. Not well known, at least in any
quantitative way, is how the inherent
2.4
unsteadiness of those processes affects
the jam formation and thickness profile.
10 min
2.2
In particular, virtually nothing is known
about the effect of ice momentum on jam
0
2.0
40
formation and thickening. This study
presents the first formulation and exami-
1.8
nation of the fully coupled dynamic na-
ture of the unsteady processes associated
1.6
with jam formation. It does so by means
0
1000
2000
3000
4000
5000
x Location (m)
of numerical simulations and laboratory
Figure 65. Effect of ts on final jam thickness flume experiments. The experiments
also show that equilibrium thickness for-
profile shape.
mulations consistently underestimated
measured jam thickness.
The numerical simulation uses the full one-dimensional unsteady flow equa-
tions (conservation of mass and momentum) for water flow, ice movement, and
jam formation. A unique aspect of the simulation is that the equations are solved in
a fully coupled manner. The simulation model is shown to be robust, versatile, and
accurate in calculating jam thickness profile under a variety of initial jam, flow, and
channel conditions. The effects of the shape of the inflow water hydrograph on jam
thickness profile are investigated and shown to be important. A dimensionless pa-
76
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