Mississippi
Illinois
Dam 24
River
River
Flow
Missouri
Flow
River
Flow
Alton
Dam 25
Illinois
Columbia
Dam 26
Booneville
(26)
(403)
314
St. Charles
289
St. Louis
Hermann
(158)
Jefferson City
Kaskaskia
Flow
(232)
Meramek
River
258
River
230
Flow
200
Big Muddy
River
Chester
Middle
175
Mississippi
163
Missouri
River
Flow
129
113
100
Rock
Cape Girardeau
}
Gorge
n km Above the Ohio River
84
n
Ohio
n km Above the Missouri-Mississippi River Confluence
Flow
(n)
River
Commerce
21
River Gaging Station
Cairo
Birds Point
0
10
20
30 mi
3.2
N
0
50 km
Flow
Figure 1. Middle Mississippi and lower Missouri Rivers. (From Tuthill and Mamone 1998.)
that the speed of the stress wave in the ice layer is not
motion, were derived on the basis of one-dimensional
related to the speed of water waves. As a result of this
formulations. These theories have been used
independence, water and ice flow equations need not
successfully to determine ice jam thickness along a river.
be solved simultaneously. Moreover, the speed of
Flato and Gerard (1986) and Beltaos (1993b) developed
characteristic waves of the water and ice equations can
one-dimensional numerical models for computing the
be significantly different. The temporal and spatial
configuration of static ice jams. Beltaos' model is also
discretizations in the numerical solutions have to be
capable of simulating grounded jams. Since the
treated with care. More recently, Zufelt and Ettema
dynamics of the ice movement and flow were not
(1997) used a simplified one-dimensional formulation
considered, the static ice jam theories cannot explain
to study the dynamic effect on ice jam thickness profiles
the formation of ice jams. They also cannot determine
in prismatic channels. They used the Mohr-Coulomb
whether, when, and where a jam will form. Moreover,
law for static passive granular accumulation to describe
the momentum effects of ice and water flows on the ice
the internal ice stress.
jam evolution and thickness were not accounted for in
One-dimensional models have limited applicability,
the static ice jam theories.
as river ice transport and ice jam evolution are two-
Shen et al. (1990) developed an analytical frame-
dimensional phenomena attributable to the existence
work for the dynamic transport of river ice and ice jam
formation and evolution. Lal and Shen (1991)
et al. (1993) developed a two-dimensional dynamic river
developed a numerical model for simulating dynamic
ice transport model, which was successfully used to
ice transport and ice jam evolution in river channels
study the dynamics of ice transport and jamming in the
and showed the importance of the inertia effect on ice
upper Niagara River (Su et al. 1997, Lu et al. 1999). It
jam configuration. They also showed that the water
wave speed is not affected by the ice conditions, and
was also modified and applied to study the transport of
2
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