used had the following properties: median diameter d50 = 1.28 mm, geometric stan-
dard deviation = 1.22, and specific gravity = 2.71. The sand was immobile for the
modeling flows used.
For the setup depicted in Figure 11, the model might be likened, in approximate
terms, to the confluence of the Mississippi and Missouri Rivers, though vertically
distorted in scale. Relative to those rivers, the model's approximate scales are 1:1,000
for horizontal lengths and 1:450 for vertical lengths.
Model scales for flow and velocities were selected in accordance with the simil-
itude criterion based on densimetric Froude number,
Vr
=1
(∆ρ / ρ)r grYr
where V = velocity,
Y = flow depth,
∆ρ = ρ ρi,
ρ = density of water,
ρi = density of ice,
and subscript r implies scale ratio (prototype/model).
This criterion leads to a velocity scale Vr = Yr0.5 ≈ 21, and a time scale for horizontal
travel ratio, tr = XrYr0.5 ≈ 47, for the length scales given above and (∆ρ/ρ)r = 1 = gr.
Confluence configurations modeled
The following confluence configurations were modeled:
Channel widths--b1, b3 = 217 to 480 mm; b2 = 160 to 217 mm.
Channel depths--Y1 = Y2 = 25 to 50 mm.
Confluence apex angle--α = 0 to 180.
Confluence external angle--θ = 90 to 180.
The modeling program encompassed the range of combinations of these chan-
nel configurations. The results of all combinations were not recorded in detail, as
many combinations produced more or less the same ice movement and jamming
behavior. Selected cases were investigated in closer detail when they showed dis-
tinct differences in jam formation.
Model ice
Ice was modeled using polypropylene beads whose average diameter is 3 mm
and whose specific gravity is 0.90. The beads are approximately spherical in shape.
Model channel width relative to model ice piece diameter, b/D, varied from about
53 to 160. Model channel depth relative to model ice piece diameter, Y/D, varied
from about 7 to 15.
The model ice was fed manually into each confluent channel. As the emphasis
of the tests was on identifying the mechanisms of ice jamming in confluences, the
model ice discharge into the channels was measured imprecisely. In fact, the con-
ditions for confluence jamming revealed by the tests indicated that limits to ice
passage through a confluence can be calculated quite directly. Therefore, there
was little need for accurate measurement of ice discharge rates.
24
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