The weight of the cover in the downstream direction *f*3 can be defined as

(12)

where *R*H is the total hydraulic radius beneath the ice. Substituting eq 11 and 12

into 10, and dividing by *H*2 (*H *= the open water depth just upstream of the ice

cover), renders eq 10 dimensionless, i.e.

η

η2

2τc η

+ *s*i (1 - *s*i ) 2 .

1 + *s*i

=

(13)

Equation 13 can be used to predict ice thickness for the wide-jam case. Pariset et al.

recognized that freeze-bond forces are of lesser importance for thicker jams, and

are not important during breakup conditions, because jam resistance is dominated

by gravitational effects, i.e., ice weight. They developed a dimensionless stability

parameter *X *to relate jam thickness to upstream open-water conditions:

2

3

η

η

1 - *s*i

*H*

2

2

= 2o2 =

η

(14)

24

1 + *s*i

where *Q *is water discharge and *u*o is bulk open water velocity for uniform flow far

upstream of the jam. Values of *X *are plotted in Figure 14 for *s*i = 0.92 and = 1.28,

which are values adopted by Pariset et al. for jams in the St. Lawrence River. The

figure indicates jams as being stable (inside the bell curve) or unstable (outside the

curve). The curve is useful, but it does not enable direct calculation of ice thickness.

Moreover, it assumes equilibrium conditions, i.e., steady, uniform flow of water

and uniform ice thickness.

Uzuner and Kennedy (1976) presented a detailed formulation of the time-

dependent differential equations describing the force equilibrium in a static, float-

ing ice jam. Their formulation is

3

3 x 10

2

Unstable

Stable

Region

Region

1

0

0.4

0.8

1.2

η/H

15

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