360

Jam Releases

300

240

180

Daily Average Flow = 140 m3/s

120

Jam Forming

(0700 hr)

60

0

6

12

18

6

12

18

6

12

18

March 10

March 11

March 12

discharge at upstream locations, however, could be markedly different from that

recorded at the gauge. In many cases, gauges are not located near the jammed reach

and estimates of discharge become difficult. In some situations, a jam may create a

backwater effect on the measuring gauge, and interpretation of the stage recording

(in developing the discharge record) also becomes questionable. Winter discharge

estimates can be off by as much as 25% because of backwater from ice jams. As a

result, the choice of discharge used in a steady-state model can greatly affect the

results of the modeling.

The fully coupled model was used, in conjunction with the static-unsteady thick-

ness model with a constant discharge, to determine how the choice of water dis-

charge affects jam thickness profile. Figure 55 shows a hypothetical breakup jam

discharge hydrograph. The hydrograph is characterized by a fast rise and very

short duration peak, similar to the hydrograph depicted in Figure 54. While the

fully coupled model uses this hydrograph as an upstream boundary condition, a

steady-state model requires that a single discharge be chosen as an input variable.

One choice might be the peak value of discharge. If the modeled system were of

significant length, however, the instantaneous peak would be attenuated as it trav-

eled downstream. Thus, the discharge felt at downstream locations (and conse-

quently shear stress on the underside of the jam) would be less.

Another choice for the steady-state discharge might be a time-averaged discharge

based on the time required for a disturbance to pass through the system. Two tests

were run with the static-unsteady thickness model at a constant discharge level

and corresponding uniform values of depth and water velocity. This simulated the

calculations of a steady-state model: one with a constant discharge of the peak

value of 200 m3/s from Figure 55 and the other with a time-averaged constant

discharge value of 167 m3/s.

Figure 56 shows the final jam thickness profiles for these two runs, along with

the final jam thickness profile predicted using the fully coupled model with the

unsteady discharge hydrograph. The steady discharge levels and uniform initial

conditions result in uniform jam thickness equal to that given by the equilibrium

jam formulation represented by eq 25. The fully coupled thickness profile is greater

than the equilibrium thickness for both of the steady discharge choices everywhere,

70

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