The effects of the ice-weighting fac-
tor were then investigated by running
the baseline conditions with θ = 0.6 and
θi = 0.5, 0.55, 0.6, 0.66, and 0.80. Again,
with a value of θi = 0.5, the solution be-
came highly unstable and gave unrea-
sonable results in terms of ice thickness.
Figure 45 shows the final jam thickness
profile for θi = 0.55, 0.6, 0.66, 0.8, and 1.0.
The profile shows little variation with
x Location (m)
θi = 0.6, providing physically reasonable
Figure 45. Final jam thickness profiles for
results. Inspection of the values of the
θ = 0.6 and θi = 0.55, 0.6, 0.66, 0.8, and 1.0.
other dependent variables throughout
the simulations showed that either θi =
0.6 or 0.66 would be acceptable. For the
remainder of the model testing, the val-
ues of θ = 0.6 and θi = 0.6 were used.
Alternate boundary conditions
Final Ice Bottom
The boundary conditions for the
Initial Ice Bottom
baseline runs included specified water
discharge and equilibrium thickness at
the upstream end, and zero ice velocity
and a condition of normal flow depth
x Location (m)
beneath the jam at the downstream end.
Figure 46. Final bed, bottom of jam, and wa- While these boundary conditions repre-
ter surface level profiles for the condition of sent plausible natural conditions, they
downstream depth being held at 3.0 m.
are by no means all inclusive. A dam, for
instance, typically has a water surface
slope that decreases in the downstream direction and results in downstream water
levels that are significantly above the normal depth. Ice jams in dam pools often are
resistant to shoving and thickening because of the reduced shear stress and gravity
forces exerted on them. The equilibrium jam thickness at the upstream end also
implies that there is an unlimited supply of ice upstream of the jam that would
continually move into the modeled reaches at the equilibrium thickness.
Two alternative boundary condition types were developed. A condition of speci-
fied ice thickness at the upstream end of the jam facilitates simulation of the upper
transition zone where jam thickness is reduced. The effects of lower upstream jam
thickness on the shape of the final jam thickness profile can also be investigated. A
condition of specified water depth at the downstream end of the system facilitates
simulation of ice jams in reservoirs or at other water-elevation control structures.
A run was carried out to simulate jam shoving and thickening in a reservoir
where the downstream depth was held at 3.0 m. The initial water depths and
velocities for this run were determined by running a steady water discharge of 100
m3/s with a uniform depth throughout the 3.0 m and letting the system attain
steady flow conditions. The baseline inflow hydrograph was then run with all other
parameters the same as for the baseline test. Figure 46 shows the initial and final
water surface, and the bottom profiles of the jams. The downstream end experi-
enced no shoving and thickening, remaining at the initial thickness of 1.45 m, while