In eq 25, the terms (reading from left to right) are Fdrag, Fweight, Fstrength, Fbank,
F ′ / b2 , and Ff′′ w2 / b2 . This formulation is approximate, but it facilitates esti-
lo
flow2
mation of the confluence flow conditions needed for flow from one channel to
impeded ice movement from the second channel. It would, of course, have to be
adjusted to take into account other confluence geometries.
3. Jamming due to a confluence bar
The third mechanism for jam formation also can be formulated in an approxi-
mate manner. The likelihood of ice pieces arching across the narrowest section of
a confluence, as in Figure 32, can be estimated using the estimation relationship
channels. The likelihood that a thickened layer of ice will jam at the narrowest
section of the confluence can be estimated by estimating the thickness of accumu-
lated ice needed to jam in a channel of width equal to bc = b3 bs. Jamming will
occur if the thickness is less or equal to an accumulation thickness estimate based
on equivalence of cross-sectional areas of ice confluent into a flow channel of width
b3 bc; i.e.,
1
(b1η1 + b2 η2 ) ≤ ηeq
ηc =
(26)
bc
conveying a flow rate = Q1 + Q2.
Equation 26 can be used together with an equation for ηeq, as an approximate
means to estimate jamming conditions for a range of geometric and flow condi-
tions.
ICE JAMS IN THE CONFLUENCE OF
MISSISSIPPI AND MISSOURI RIVERS
Though ice jams form at intermittent frequencies in the confluence of the Mis-
sissippi and Missouri Rivers, they cause expensive disruptions to navigation on
the Mississippi River and usually damage tow barges moored in fleeting areas
along the Mississippi and Missouri Rivers. Figure 33, for example, depicts a jam at
the confluence during February 1989.
The St. Louis District of the U.S. Army Corps of Engineers, the agency charged
with maintaining navigation through the confluence reach of the Mississippi, needs
to know how ice jams form at the confluence of the Mississippi and the Missouri
Rivers. A major factor affecting jam formation appears to be a large bar, which is
evident in the aerial photograph Figure 33. The likely mechanism causing ice jam-
ming is ice congestion at the section of the confluence narrowed by the bar. The
Corps recognizes that the bar partially impedes ice movement through the conflu-
ence and wishes to confirm that reducing its size would significantly improve ice
movement through the confluence. The method selected and already partially
implemented for reducing the extent of the bar entails the placement of bendway
weirs through a portion of the confluence. The St. Louis District of the Corps wished
also to confirm that the bendway weirs would create no inadvertent adverse effect
on ice movement through the confluence.
The modeling work presented here was aimed at establishing the general fea-
tures of ice movement and ice jamming in the MississippiMissouri confluence
41
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