240

except the most downstream reaches.

The effects of ice momentum and

200

nonuniformities in depth and thickness

on the fully coupled profile are clearly

160

evident, even for this discharge

hydrograph with a very short duration

120

peak. The smaller thicknesses at the

downstream end are ascribable to at-

80

tenuation of the peak flow as it travels

0

100

200

300

400

500

600

Time (min)

downstream. Figure 57 shows the dis-

charge hydrograph at the upstream

boundary, the midpoint of the modeled

system, and the downstream boundary.

The peak flow is greatly reduced as it

travels downstream, with a maximum

value less than 150 m3/s by the time it

reaches the midpoint of the modeled

system. The wave is also significantly

flattened. The high-frequency fluctua-

tions in discharge at the mipoint come

from ice movement. As the ice moves

and stops, resistance to water flow var-

ies, resulting in local fluctuations in wa-

ter discharge.

The numerical experiments show that

ice momentum is important in the pre-

200

diction of jam thickness. Its effect can be

a large one, not only in the magnitude

Upstream

of the thickness as compared to that pre-

160

dicted by equilibrium theory, but also in

the nonuniform shape of the thickness

Mid-reach

profile. Some of the experiments show,

120

Downstream

however, that, for small changes in the

discharge or for initial conditions of jam

thickness that are slightly less than equi-

80

0

100

200

300

400

500

600

librium thickness associated with the ex-

Time (min)

pected flow levels (e.g., those presented

in the *Model Rigor *section), ice momen-

tum has a negligibly small effect.

For example, the final jam thickness

profile in Figure 42 is within 10% of the

equilibrium thickness value for that water flow rate, for the jam with an initial

thickness of 1.3 m. The average jam thickness, however, is 1.5 m or 2% above the

equilibrium value. For this case, a steady-state equilibrium thickness calculation

would have proved satisfactory. When unsteady boundary condition data are not

available, it may be necessary to use a simpler steady-state model to provide jam

thickness estimates, rather than using the fully coupled unsteady model. There-

fore, it is useful to identify a parameter, or set of parameters, that indicate when ice

71