240

(156)

200

where *L*T is the total length of the mod-

eled system. Runs were made for the

160

values of *t*p given above and three dif-

5 min

10

ferent bed slopes--0.00005, 0.0005, and

20

40

0.001. A functional relationship between

120

80

the ratio of average final jam thickness

160

80

0

100

200

300

400

500

600

Time (min)

to peak *t*p increases, the average final jam

thickness η approaches that predicted

by equilibrium theory ηeq. The effects of

1.6

profile is demonstrated in Figure 62,

Bed Slopes

which shows the final profiles for times

0.00100

to peak of 5, 20 (standard), and 80 min-

0.00050

0.00005

1.4

utes for the bed slope of 0.0005. As *t*p

η

decreases, the changes in water dis-

η eq

charge for each time step increase, result-

1.2

ing in larger gradients of the variables

in the upstream reaches. The gradient

terms (e.g., η/ *x *) are not included in

1.0

the equilibrium thickness formulation of

0

4

tb 8

12

eq 25 and play an important part in the

tp

full ice momentum equation. Also, the

large changes in water discharge easily

tp/tb at three bed slopes.

overpower the stability of the jam, result-

ing in significant ice velocities and ice

momentum effects.

3.2

Experiments were also conducted to

investigate the effects of the sustained

2.8

time at the peak flow *t*s. For these runs,

5 min

the standard inflow hydrograph rate of

rise of 2.5 m3/s increase per time step

2.4

20

was used, but the time at which the wa-

ter flow was held at 200 m3/s, before be-

2.0

80

ing reduced back to the initial value of

100 m3/s, was varied. The sustained

1.6

0

1000

2000

3000

4000

5000

times simulated were 0 (instantaneous

x Location (m)

peak), 10, 20, 40, 80, and ∞ minutes (no

discharge decrease) as shown in the in-

flow hydrographs depicted in Figure 63.

These runs were conducted at the same

three bed slopes as above.

Figure 64 shows relationships between the ratio of final average thickness to

nal value of *t*s/*t*b (beyond which there were no changes in jam thickness) was cho-

sen for plotting purposes. Again, the effect of bed slope is clearly seen. It is signifi-

cant that, as the value of *t*s/*t*b reaches 1, the effects of further increases in the

75